Electrostrictive compound actuator

ABSTRACT

The present invention presents a system for a compound actuator. The system includes first and second electrode layers each including two electrode sections, an intermediate electrode layer between the first and second electrode layers, and first and second electrostrictive materials that change length in an applied electrical field. The first electrostrictive material is positioned between the first and intermediate electrode layers. The second electrostrictive material is positioned between the intermediate and second electrode layers. The first electrostrictive material has a first length adjoining the first electrode section and a second length adjoining the second electrode section. The second electrostrictive material has a third length adjoining the fourth electrode section and a fourth length adjoining the fifth electrode section. The first and second electrostrictive materials are attached such that differential changes in the first and third lengths, and the second and fourth lengths, respectively, results in a compound lateral motion.

RELATED APPLICATION

This application is a continuation-in-part of the patent applicationSer. No. 10/286,097 filed on Oct. 31, 2002, and entitled “ElectricalSystem for Electrostrictive Bimorph Actuator.”

GOVERNMENT LICENSE RIGHTS

This invention was made with Government support under U.S. Governmentcontract awarded by the Department of the Army, DADD-19-99-C-0023. TheGovernment has certain rights in this invention.

FIELD OF THE INVENTION

This invention relates generally to electrostrictive materials and, morespecifically, to actuators based upon electrostrictive materials.

BACKGROUND OF THE INVENTION

Piezoelectric materials exhibit strain when subject to an appliedelectrical field. For example, piezoelectric materials exhibit bothelongation and contraction when subject to varying electrical fields. Asa result, piezoelectric materials have been used in actuatorapplications where their linear relationship of strain to the appliedfield is exploited to create both elongation and contraction, therebycreating a bi-directional actuator.

Recent advances in the fields of piezoelectric and ferroelectricresearch have lead to the discovery of new materials exhibiting evenlarger but electrostrictive or contractive strain. In particular,electrostrictive crystals such as Lead Magnesium Niobate-Lead Titanate[PMN-PT], Lead Zinc Niobate-Lead Titanate [PZN-PT], andelectron-irradiated copolymer poly (vinylidenefluoride-trifluoroethyline) [P(VDF-TrFE)], exhibit large energydensities and recoverable strains of 1% to 4%. In general, the higherstrain capacity and energy density of electrostrictive materials (ascompared to piezoelectric materials) make them attractive replacementsfor piezoelectrics in actuators. For example, the strain coefficient forthe piezoelectric polyvinylidene fluoridine is less than 10% of thestrain coefficient for the electrostrictive irradiated P(VDF-TrFE).

However, electrostrictive materials only exhibit unidirectional straineven when polarity of the applied electrical field is reversed. Due tothis feature, only unimorph or one-directional electrostrictiveactuators have been created. Unimorph electrostrictive actuatorstypically include a passive restoring layer. This passive layer reducesthe active portion of the actuator, and thus decreases the total energydensity of the actuator. If the entire actuator could be active, anelectrostrictive bimorph or bi-directional actuator could theoreticallyexceed the performance of a similar piezoelectric bimorph actuator by afactor of at least 5. However, a fully active bimorph electrostrictiveactuator would have to compensate for the material having onlyunidirectional strain.

Therefore, there is an unmet need for bimorph or bi-directionalactuators using electrostrictive materials.

SUMMARY OF THE INVENTION

The present invention provides bimorph actuation of systems utilizinghigh-density electrostrictive materials, thereby permitting the size andweight of electrically driven actuators and arrays of actuators to bereduced.

The present invention presents a system for a compound actuator. Thesystem includes first and second electrode layers each including twoelectrode sections, an intermediate electrode layer between the firstand second electrode layers, and first and second electrostrictivematerials that change length in an applied electrical field. The firstelectrostrictive material is positioned between the first andintermediate electrode layers. The second electrostrictive material ispositioned between the intermediate and second electrode layers. Thefirst electrostrictive material has a first length adjoining the firstelectrode section and a second length adjoining the second electrodesection. The second electrostrictive material has a third lengthadjoining the fourth electrode section and a fourth length adjoining thefifth electrode section. The first and second electrostrictive materialsare attached such that differential changes in the first and thirdlengths, and the second and fourth lengths, respectively, results in acompound lateral motion.

According to other aspects, the present invention provides a system ofelectrodes for a compound actuator, a recurve actuator, a multi-layeractuator, an actuator array, and methods for actuating compoundactuators and arrays. The present invention may be utilized to generatea synthetic jet for aeronautical or other purposes.

BRIEF DESCRIPTION OF THE DRAWINGS

The preferred and alternative embodiments of the present invention aredescribed in detail below with reference to the following drawings.

FIG. 1A is a side perspective view of the bimorph actuator connected toan exemplary drive circuit;

FIG. 1B is a top view of the bimorph actuator connected to an exemplarydrive circuit;

FIG. 1C is a plot of voltage versus time for the bimorph actuator;

FIG. 2A is a top view of the first, second, and third electrodes inassembled configuration;

FIG. 2B is a top view of the individual first, second and thirdelectrodes;

FIG. 3 is a plot of voltage versus strain showing strain derived fromthe applied voltages;

FIG. 4A is a side view of the present invention;

FIG. 4B is a side view showing bending of the present invention;

FIG. 4C is a side view showing opposite bending of the presentinvention;

FIG. 5 is a cross-section of an energy sampler driven by the presentinvention;

FIG. 6A is a side perspective view of a recurve actuator;

FIG. 6B is a top view of a recurve actuator connected to an exemplarydrive circuit;

FIG. 6C is a symbolic side view of a recurve actuator;

FIG. 7A is a side view of a recurve actuator of the present invention;

FIG. 7B is a side view of a recurve actuator of the present inventionshowing bending;

FIG. 7C is a side view of a recurve actuator of the present inventionshowing opposite bending;

FIG. 8A is a top view of the first, second, and third electrode sheetsof a recurve actuator in assembled configuration;

FIG. 8B are top views of the individual first, second, and thirdelectrode sheets of a recurve actuator;

FIG. 9A is a side view of a recurve actuator array of the presentinvention in expanded configuration;

FIG. 9B is a side view of a recurve actuator array of the presentinvention in contracted configuration;

FIG. 10A is an exploded perspective side view of a multi-layer recurveactuator of the present invention;

FIG. 10B is a symbolic side view of the electrode configuration of amulti-layer recurve actuator;

FIG. 11 is an perspective side view of the electrode sheets andelectrical connections for a multi-layer recurve actuator;

FIG. 12A is a cross-section of a synthetic jet driven by a recurveactuator array of the present invention in its neutral configuration;

FIG. 12B is a cross-section of a synthetic jet driven by a recurveactuator array in its extended configuration;

FIG. 12C is a cross-section of a synthetic jet driven by a recurveactuator array in its retracted configuration;

FIG. 13A is a side view of a compound actuator of the present invention;

FIG. 13B is a side view of a compound actuator showing bending;

FIG. 13C is a side view of a compound actuator showing opposite bending;

FIG. 14A is a symbolic side view of the electrode configuration of acompound actuator of the present invention; and

FIG. 14B is a top view of the individual electrode sheets of a compoundactuator of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

By way of overview, the present invention presents a system for acompound actuator. The system includes first and second electrode layerseach including two electrode sections, an intermediate electrode layerbetween the first and second electrode layers, and first and secondelectrostrictive materials that change length in an applied electricalfield. The first electrostrictive material is positioned between thefirst and intermediate electrode layers. The second electrostrictivematerial is positioned between the intermediate and second electrodelayers. The first electrostrictive material has a first length adjoiningthe first electrode section and a second length adjoining the secondelectrode section of the first electrode layer. The secondelectrostrictive material has a third length adjoining the fourthelectrode section and a fourth length adjoining the fifth electrodesection of the second electrode layer. The first and secondelectrostrictive materials are attached such that differential changesin the first and third lengths, and the second and fourth lengths,respectively, results in a compound lateral motion.

Other embodiments of the present invention provide a system ofelectrodes for a compound actuator, a recurve actuator, a multi-layeractuator, an actuator array, and methods for actuating compoundactuators and arrays. The present invention may be utilized to generatea synthetic jet for aeronautical or other purposes.

As a result, the present invention advantageously provides bimorphactuation of systems utilizing high-density electrostrictive materials,thereby permitting the size and weight of electrically driven actuatorsand sensors to be reduced.

FIG. 1A is a perspective side view of a system 5 of an exemplary bimorphactuator of the present invention connected to an exemplary drivecircuit. An electrode 14 is sandwiched between a layer 12 ofelectrostrictive material and a layer 16 of electrostrictive material. Asecond electrode 10 is arranged against the layer 12, sandwiching thelayer 12 between the electrode 14 and electrode 10. A third electrode 18is arranged against the layer 16 to sandwich the electrostrictive layer16 between the electrode 14 and electrode 18. Layer 12 and the layer 16are suitably electrostrictive materials that contract when subjected toan electrical field.

Suitable electrostrictive materials include electrostrictive crystalssuch as Lead Magnesium Niobate-Lead Titanate [PMT-PT], Lead ZincNiobate-Lead Titanate [PZN-PT], and electron irradiated copolymerpoly(vinylidene fluoride-trifluoroethyline) [P(VDF-TrFE)]. Otherelectrostrictive materials include grafted elastomers, ceramicelectrostrictors, other relaxor ferroelectric-ferroelectric solid-statesolutions, ionic polymers, and PVDF terpolymers. In one presentlypreferred embodiment, the layer 12 and the layer 16 are sheets ofirradiated P(VDF-TrFE). Relaxor ferroelectric-ferroelectric solid-statesolutions are a family of electrostrictive crystals including PZN-PT andPMT-PT as well as other complex perovskite crystal analogs. It will beappreciated that the electrostrictive materials act as dielectrics, anddo not conduct appreciable current.

The electrodes 10, 14, and 18 may be any suitable electrical conductorincluding without limitation gold, copper, or aluminum. The electrodes10, 14, and 18 may be sheet conductors, or may be conductors that aresputtered or chemically vapor-deposited on the electrostrictivematerial. In one presently preferred embodiment, the electrodes 10, 14,and 18 each include sheets of electrically conductive material, such ascopper or the like.

The electrode 10, layer 12, electrode 14, layer 16, and electrode 18 maybe assembled by any suitable method that links the layer 12 to the layer16 such that differential changes in length between the layer 12 and thelayer 16 cause the bimorph actuator system 5 to move laterally bybending. In one exemplary embodiment, the electrode 10 is fastened tothe layer 12, the layer 12 is fastened to the electrode 14, theelectrode 14 is fastened to the layer 16, and the layer 16 is fastenedto the electrode 18 suitably using thin-film adhesive. Any suitablemethod of fastening may be utilized, including without limitationthin-film adhesive, double-stick films, RBC epoxy, or applied adhesive.In one embodiment, an acceptable adhesive includes Spurr Epoxymanufactured by Poly Sciences, Inc. In another exemplary embodiment, thethin-film adhesive is a double-stick acrylic film with adhesive on bothsides. Any suitable attachment, including mechanical attachments orfasteners, such as non-conducting rivets or pins, may be suitably usedto connect the layer 12 to the layer 16 so that differential changes inthe respective lengths of the layer 12 and the layer 16 cause the system5 to move laterally by bending. For example, if one end of the system 5is restrained, bending causes lateral motion of the unrestrained end. Ifboth ends of the system 5 are restrained from moving laterally, themiddle section will move laterally as the system 5 bends. This lateralmotion or bending suitably may be used to drive mechanical systems.

The electrode 10 and the electrode 18 are connected to a voltage source38. The voltage source 38 generates an electrical field between theelectrode 10 and the electrode 18. In an exemplary embodiment, thevoltage source 38 is a DC voltage source that induces a constantelectrical field through the layer 12 and the layer 16, suitablyshortening the layer 12 and the layer 16.

The electrode 14 is also connected to a voltage source, such as a biasvoltage source 40 and an AC voltage source 42. The bias source 40 andthe AC source 42 cooperate to apply a varying voltage to electrode 14.Changing the voltage applied to the electrode 14 results in a differentelectrical field being applied to the layer 12 than is being applied tothe layer 16. As the electrostrictive materials in the layer 12 and thelayer 16 respond differently to different electrical fields, the lengthsof the layer 12 and the layer 16 differ, and the system 5 bends. Thevoltage applied to the electrode 14 suitably may be a variable voltageif controlled bending of the system 5 is desired. If periodic motion ofthe system 5 is desired, the voltage applied to the electrode 14suitably may be a biased AC source such as that generated by the biassource 40 and the AC source 42 shown in FIG. 1A.

The electrode 18, one terminal of the DC voltage source 38 and oneterminal of the bias source 40 and the AC source 42 are suitablyconnected to a ground terminal 44.

FIG. 1B shows a top view of the bimorph actuator system 5 illustrating asuitable method of connecting the electrode 10, electrode 14, andelectrode 18 to their respective power supplies. In this embodiment, theelectrode 10 and electrode 18 are connected to separate terminals of thevoltage source 38, respectively. The electrode 14 is connected to oneterminal of the bias source 40. The other output terminal of the biassource 40 is connected to a terminal of the AC source 42. Anotherterminal of the AC source 42 is connected to the electrode 18. Theelectrode 18 is also connected to a ground terminal 44.

FIG. 1B also illustrates the power connections to the electrode 10,electrode 14, and electrode 18. The connection may include any suitableelectrical connection including riveting, soldering, plug and socket,and screw terminal connections. In this exemplary embodiment, aconnection 20 to the electrode 10, a connection 22 to the electrode 14,and a connection 24 to the electrode 18 suitably do not overlap.Instead, they are aligned on a connection end 28 of the bimorph actuatorsystem 5, with the connection 22 to the electrode 14 intermediate theconnection 20 for the electrode 10 and the connection 24 for theelectrode 18. It will be understood that any suitable circuitry and anysuitable arrangement of connections and connection types that permitapplying an electrical base field to the electrode 10 and the electrode18 while providing a variable voltage to the electrode 14 will suitablyactivate the bimorph actuator system 5.

FIG. 1C is a plot of voltage V over time “t” showing the differentvoltages applied by the DC voltage source 38, and the bias source 40 andAC source 42, to the electrodes of the bimorph actuator system 5 asshown in FIGS. 1A and 1B. The voltage source 38 applies a DC voltagedifferential to the electrode 10 and electrode 18 such that voltageV_(a) at the electrode 10 is greater than voltage V_(c) at the electrode18. In this example, V_(a) and V_(c) are constant over time. VoltageV_(b) applied to the electrode 14 varies over time. In this example, thevoltage V_(b) is a biased AC voltage varying periodically between V_(a)and V_(c). When V_(b) equals V_(a) plus V_(c) divided by two (2),voltage V_(ab) across the layer 12 equals voltage V_(bc) applied acrossthe layer 16. As the voltage V_(b) rises, the voltage V_(ab) falls,while the voltage V_(bc) rises. Conversely, as the voltage V_(b) drops,the voltage V_(bc) drops, while the voltage V_(ab) increases.

In FIG. 1C, the voltage V_(b) is a periodic biased AC voltage and thusV_(ab) is a sine wave function. V_(bc) is the inverse of the V_(ab)curve, inverted around the average voltage V_(a) plus V_(c) divided bytwo. It can be seen from FIG. 1C that as the voltage differential, andhence the electrical field across one of the electrostrictive layers isincreasing the voltage differential and hence the electrical fieldacross the other electrostrictive layer is decreasing, and vice-versa.

FIG. 2A shows a top view of an exemplary embodiment of the three (3)electrodes of the bimorph actuator system 5. The electrode 10 issuitably a sheet electrode and is shown in assembled top viewconfiguration covering the electrode 14 and the electrode 18. Theelectrostrictive layers 12 and 16 are not shown. All of the connectionsto the electrodes are at a connection end 28 of the bimorph system 5.Each electrode has a tab with a connection. The electrode 10 has a tab21 with a connection 20. The electrode 14 has a tab 23 with a connection22. The electrode 18 has a tab 25 with a connection 24. The tabs andconnections are all aligned along the connection end 28 of the bimorphsystem 5. The tab 23 is located intermediate tab 21 and tab 25, and thelateral edges 26 of the tab 23 are adjacent to tab 21 and the tab 25. Asnoted, any suitable alignment of electrode connections, tab shapes, andtab connection methods may be utilized to provide appropriate voltagesto the electrodes 10, 14, and 18.

FIG. 2B shows an exemplary configuration for the individual electrodes10, 14, and 18, and their tabs and connections. The electrode 10,electrode 14, and electrode 18 are shown separately, that is,unassembled. The electrode 10, electrode 14, and electrode 18 all havetheir tabs and connections on the same connection end 28. In thisembodiment, the tab 21 is situated near a left edge 29 of the connectionend 28 of the electrode 10. The tab 23 is arranged near the center 30 ofthe connection end 28 of electrode 14. The tab 25 is arranged near aright edge 31 of the connection end 28 of the electrode 18. It will beappreciated that with the tab 23 arranged near the center 30 of theconnection end 28, the electrode 10 and the electrode 18 aresubstantially mirror images of each other. It will also be appreciatedthat the shapes of the electrode 10 and the electrode 18 may beswitched. In that instance, the resulting bimorph actuator system issubstantially a mirror image of the bimorph actuator system 5 shown inFIG. 2A. In this exemplary embodiment, it will be appreciated that asmirror images, the electrodes 10 and 18 may advantageously bemanufactured as identical pieces. The electrode 18 is the same as theelectrode 10 but simply flipped over. When the electrode 10, electrode14, and electrode 18 are stacked with intervening layers ofelectrostrictive material, the resulting assemblage is shown in FIG. 1A.The electrode tabs and the electrode connections are aligned on theconnection end 28 of the bimorph actuator system 5 and the connectionsdo not overlap. This facilitates electrical connection to the bimorphactuator system 5 because the electrical connections 20, 22, and 24 donot overlap or touch. Further, the electrical connections 20, 22, and 24are suitably near each other to facilitate providing power to theelectrical connections.

FIG. 3 is a plot of strain ε versus voltage V showing the operation ofthe present invention. Strain ε is approximately proportional to V². Theaccepted equation is ε=QP², where Q is the electrostrictive coefficient,with P being the polarization or charge per unit area. In an isotropicmaterial, this can be approximated as ε=QE² with E being the appliedelectrical field. At higher voltages, electrostrictive materials canapproximate linear responses to voltage changes. As shown in FIG. 3,electrostrictive materials have a negative strain ε in response to bothpositive and negative voltages. Strain ε as a function of voltage isthus always negative for electrostrictive materials. Contraction ornegative strain ε increases with increasing positive voltage orincreasing negative voltage. In the example shown in FIG. 3, when thevoltage V_(ab) across the first electrostrictive layer 12 is equal tothe voltage V_(bc) across the second electrostrictive layer 16, thelayer 12 and the layer 16 have equal generated strain if they originallyhave equal length and are made of the same material or respond equallyto the same applied voltage. Thus, when applied voltage V_(ab) equalsV_(bc), the layer 12 and the layer 16 still have the same length.

In the actuator system shown in FIG. 1A and FIG. 1B, an additionalbiased AC voltage is applied to the electrode 14. This applies anincreasing voltage across the layer 12 when a decreasing voltage isapplied across the layer 16. When this occurs, strain on the layer 12increases, and strain on the layer 16 decreases. Because the strain isnegative, the layer 12 shortens and the layer 16 lengthens from theirrespective identical lengths when V_(ab) equals V_(bc). The length ofthe layer 12 becomes less than that of the layer 16 and the assemblagebends. Conversely, as V_(ab) decreases with the result that V_(bc)increases, with strain being negative with increasing voltage, the layer16 shortens while the layer 12 lengthens. The assemblage then bends inthe opposite direction. By way of example, electrical fields suitablyapplied to sheets of irradiated P(VDF-TrFE) are approximately 1 to 200million volts per meter. If a periodic motion of the actuator isdesired, the frequency of the AC voltage applied may range from nearlyDC to up to 10 kilohertz. There is no known lower limit to how slowlythis configuration can actuate.

FIGS. 4A, 4B, and 4C show the actuator system 5 in operation. If one endof the bimorph actuator system 5 is held in a holder 34, the otherunrestricted end 36 deflects as varying voltages are applied to theelectrostrictive materials. In FIG. 4A, the voltage V_(ab) across thelayer 12 is equal to the voltage V_(bc) across the layer 16. Because thevoltage V_(ab) is equal to the voltage V_(bc), both layers 12 and 16have the same length, and the system 5 is straight. In the embodimentshown in FIG. 4A, the electrodes 10, 14, and 18 are thin, sheet metalelectrodes. The electrostrictive material layers 12 and 16 are thinsheets of irradiated P(VDF-TrFE) that have equal length before anyelectrical field is applied. In this embodiment, the electrode 10 isattached to the layer 12, the layer 12 is attached to the electrode 14,the electrode 14 is attached to the layer 16, and the layer 16 isattached to the electrode 18 with double-stick adhesive sheets (notshown).

FIG. 4B shows deflection of the bimorph actuator 5 when the voltageapplied to the electrode 14 is decreased. This increases the voltagedifference V_(ab) between the electrode 10 and the electrode 14 anddecreases the voltage difference V_(bc) between the electrode 14 and theelectrode 18 with the result that V_(ab) is greater than V_(bc)(V_(ab)>V_(bc)). In this instance, the layer 12 contracts relative toits length shown in FIG. 4A, and the layer 16 expands relative to itslength shown in FIG. 4A, with the result that the bimorph actuator 5bends in a direction towards the electrode 10.

FIG. 4C shows the converse of FIG. 4B. In this instance V_(b) isincreased, with the result that the voltage difference V_(ab) betweenthe electrode 10 and the electrode 14 decreases, while the voltagedifference V_(bc) between the electrode 14 and the electrode 18increases. Again, because these are electrostrictive materials wherecontraction increases with increasing voltage and contraction decreaseswith decreasing voltage, the layer 12 lengthens and the layer 16shortens as compared to their lengths as shown in FIG. 4A when V_(ab)equals V_(bc). In this instance, the actuator bends in an oppositedirection toward the electrode 18.

It will be appreciated that the bimorph actuator system 5 may be used todrive any number of mechanical and electromechanical systems. Examplesof systems that can be driven by a bimorph electrostrictive actuatorinclude ultrasonic speakers, making and breaking electrical contacts,optical switching, and mechanical systems such as windshield wipers.

In an ultrasonic system, or in a speaker, an electrostrictive actuatorsuitably may drive a diaphragm, thereby generating electro-ultrasonicpulses or sound. In an electrical system, the electrostrictive actuatorsuitably may make or break contacts, thereby acting as a relay. In anoptical system, an electrostrictive actuator suitably may move a mirroror other optical switch, thereby switching optical transmissions. Inmechanical systems, the bimorph electrostrictive actuator may activateany suitable mechanical device. Using electrostrictive materials in abimorph actuator system permits the actuator to have a higher energydensity, or, in other words, lighter weight for the same power thancomparable piezoelectric actuators.

A bimorph actuator suitably may also be used to sample movement orgenerate power from movement. As is known, electrostrictive materialsexhibit strain when subjected to varying voltages. However,electrostrictive materials operate in a reverse direction as well,generating voltage differences when strain is applied. If a vibratingsampler is attached to a bimorph actuator, the actuator will generate avoltage differential, and that voltage differential will be higher thanthat produced by a piezoelectric actuator under the same strain. Thus, abimorph actuator may be used to sample vibrations or motion, or even togenerate power from vibrations or motion. By way of example, and not bylimitation, FIG. 5 shows an airflow sensor system 85. A suitable paddle80 is connected to a bimorph actuator 51. The paddle 80 is placed in anairflow 82 that causes deflection or vibration in the bimorph actuator51. The actuator 51 is supported by an actuator support 58 attached to aframe 52, so the paddle 80 suitably projects into the airflow 82.Deflection or vibration of the paddle 80 causes the bimorph actuator 51to deflect or vibrate, thereby generating a voltage differential. Thevoltage differential can be sampled through a power cable 54 connectedto the bimorph actuator 51. The airflow sensor system 85 can sensedeflection and vibration which can be measured by voltage derived fromthe bimorph actuator 51 through the power cable 54.

It will be appreciated that the bimorph actuator of the presentinvention may be utilized in a wide range of configurations,assemblages, and shapes depending upon the system to be driven oractuated. In one presently preferred embodiment, bimorph actuators ofthe present invention are arranged in linked segments and actuated tocurve in opposite directions to form compound actuators. One feature ofcertain compound arrangements of such actuators is that they may beconfigured to produce deflection along a line, as opposed to an arc.

FIG. 6A is a side view of an exemplary recurve actuator 105 of thepresent invention. A recurve actuator 105 is a compound actuator withthree curving bimorph actuator sections in alignment, with the two endelectrode sections configured to curve in one direction while thecentral section is configured to curve in an opposite direction. In thisexemplary recurve actuator 105, an intermediate electrode sheet 140 issandwiched between a first layer 112 of electrostrictive material and asecond layer 116 of electrostrictive material. A second electrode sheet120 is arranged against the layer 112, thereby sandwiching the layer 112between the intermediate electrode sheet 140 and the second electrodesheet 120. A third electrode sheet 160 is arranged against the layer 116to sandwich the electrostrictive layer 116 between the electrode sheet140 and the electrode sheet 160. Layers 112 and 116 are suitablyelectrostrictive materials that contract when subject to an electricalfield.

Suitable electrostrictive materials for the recurve actuator 105 are thesame as those for the embodiments of the bimorph actuator describedabove. The electrode sheets 120, 140, and 160 may be any suitableelectrical conductor sheet as described above. In the one presentlypreferred embodiment, the electrode sheets 120, 140, and 160 includesheets of copper.

The electrode sheet 120, layer 112, electrode sheet 140, layer 116, andelectrode sheet 160 may be assembled by any suitable method that linksthe layer 116 to the layer 112 such that differential changes in lengthbetween the layer 112 and the layer 116 cause the recurve actuator 105to move laterally by bending, typically in a clam-shell shaped bend or“recurve” shape. In such a bend, the first end 106 and the second end108 of the recurve actuator 105 remain in alignment, while the centerelectrode section 107 of the recurve actuator 105 deflects laterally.Reversing the electrical fields applied to electrostrictive layers 112and 116 result in an opposite lateral deflection.

Any suitable method of linking or fastening the layers 112 and 116 toeach other may be utilized, including without limitation, theattachments and adhesives suitable for the embodiments of the presentinvention described above.

Each electrode sheet of the recurve actuator 105 is divided intosections to which differing voltages are applied, thus applyingdifferent charges across adjacent segments of the electrostrictivelayers 112 and 116.

In the recurve actuator 105, the electrode sheet 120 has a first endelectrode section 122, a center electrode section 124, and a second endelectrode section 126. The electrode sections 122, 124, and 126 in apresently preferred embodiment utilize a copper conductor divided bygaps 129 in the conductor, thereby breaking the electrode sheet 120 intothe three sections. It will be appreciated that any suitable method ofdividing the conductor sections into separate areas may be utilized,including bars of insulation, or alternate layers that are notelectrically connected. It will be appreciated that the first endelectrode section 122, the center electrode section 124, and the secondend electrode section 126 are not electrically connected within theelectrode sheet 120 in this exemplary embodiment. Depending upon therecurve deflection desired, or if alternate widths or shapes of therecurve actuator 105 are utilized, the end electrode sections may beelectrically connected or otherwise linked together.

The intermediate electrode sheet 140 is divided into a first endelectrode section 142 and a second end electrode section 144 by a gap149 in the middle 107 of the electrode sheet 140. In this exemplaryrecurve actuator 105, as further described in FIG. 6B below, the gap 149separating the two electrode sections 142 and 144 facilitates theelectrical connections to the electrode sheet 120 and the electrodesheet 160. In this embodiment, both sections 144 and 142 of theelectrode sheet 140 are driven by the same voltage. Thus, a gap orseparation between section 142 and section 144, while advantageous forelectrical connections, is not required for the recurve actuator 105.

The third electrode sheet 160 is divided into three sections. Like theelectrode sheet 120, the third electrode sheet 160 has a first endelectrode section 162, a center electrode section 164, and a second endelectrode section 166. The first end electrode section 162 is separatedfrom the center electrode section 164 and the center electrode section164 is separated from the second end electrode section 166 by gaps 169.

FIG. 6B shows a top view of the exemplary recurve actuator 105 shown inFIG. 6A. The recurve actuator 105 is connected to the electrical drivecircuit as described in reference to FIGS. 1A, 1B, and 1C above. A DCvoltage 38 is applied to the end electrode sections 122, 126, 162, and166 and the center electrode sections 124 and 164 (designated “a” & “c”when driven by voltages equal to V_(a) and V_(b) respectively) of FIG.6A. A bias source 40 and AC voltage source 42 is connected to thecentral electrode sheet 140 (designated “b” when driven by a voltageequal to V_(b)). The drive system 39 is suitably connected to a groundterminal 44.

FIG. 6B, by way of example but not limitation, shows an embodiment ofthe electrode sheet configurations utilized to form a recurve actuator105 of the present invention. Electrostrictive layers 112 and 116 of therecurve actuator 105 as shown in FIG. 6A do not appear in FIG. 6Bbecause they are typically translucent or transparent. Thus, the topview of the recurve actuator 105 as shown in FIG. 6B shows the entireelectrode sheet 120, closest to the viewer, those portions of theelectrode sheet 140 not covered by the electrode sheet 120, and thoseportions of the electrode sheet 160 not covered or obscured by electrodesheets 120 and 140, looking downward through the sandwich of theelectrode sheets 120, 140, and 160, respectively.

In FIG. 6B, a V_(a) conductor 101 from the DC voltage source 38 iscoupled to the first end electrode section 122 of sheet 120 through aconnection 121. The connection 121 is further coupled to the centerelectrode section 164 of sheet 160 through a connection 163 and to thesecond end electrode section 126 of the sheet 120 through a connection125 by electrical conductor 117. It will be noted that all V_(a)connections are denoted “a” on FIG. 6B. By way of example and notlimitation, an electrical conductor 117 connecting connections 121, 163,and 125 is suitably a wire running from the first end 106 to the secondend 108. This conductor 117 advantageously allows the “a” or V_(a)sections of the recurve actuator 105 to be driven from one end—in thisinstance the first end 106. It will be appreciated that the conductor117 is connected to the connection 163 of the center electrode section164 of the electrode sheet 160 without shorting to the center electrodesection 124 of the electrode sheet 120, or electrode sections 142 and144 of the intermediate electrode sheet 140. This is because, in thisembodiment, the connection 163 is suitably situated in a notch 127defined in the center electrode section 124 of the sheet 120. Connection163 is also suitably situated in the center gap 149 in the electrodesheet 140 (not shown in this view). Thus, part of the center electrodesection 164 of the electrode sheet 160 is visible through a gap 129 inthe center electrode section 124 of electrode sheet 120, and through acenter gap 149 in the electrode sheet 140 because the conductors do notoverlap in the location of the connection 163 to the center electrodesections 164 of the electrode sheet 160. This permits the centerelectrode sections 164 of the electrode sheet 160 to be driven inparallel with the end electrode sections 122 and 126 of the electrodesheet 120 without shorting to the other electrode sections.

In FIG. 6B, the two electrode sections 142 and 144 of the intermediateelectrode sheet 140 are visible through the gaps 129 in the conductorsections of the sheet 120. The first end electrode section 142 andsecond end electrode section 144 are driven by the V_(b) conductor 102from the bias source 40 and the AC source 42 through a connection 141 tothe first end electrode section 142 and through a connection 145 to thesecond end electrode section 144. In this embodiment, the connection 141is suitably located at the end 106 of the recurve actuator 105 andconnection 145 is suitably located at second end 108 of the recurveactuator 105. The connection 145 is coupled to the connection 141through a conductor 118 running from the end 108 to the end 106 of therecurve actuator 105. By way of example and not limitation, theconductor 118 between the connections 141 and 145 is suitably a wire.This advantageously permits the sections 142 and 144 of the electrodesheet 140 to be driven from the first end 106 of the recurve actuator105. It will be appreciated that the conductor 118 may be replaced withan alternate connection between the sections 142 and 144 of theintermediate electrode sheet 140. Such a connection suitably may be aconductor bridge on the electrode sheet 140 itself.

In this embodiment, a V_(c) conductor 103 completes the drivingconnections to the recurve actuator 105 by connecting the ground 44, theDC voltage source 38, and the bias source 40 and AC source 42 to thefirst end electrode section 162 of electrode sheet 160, the centerelectrode section 124 of electrode sheet 120, and the second endelectrode section 166 of electrode sheet 160. The V_(c) conductor 103 issuitably connected through the connection 161 on the end 106 to thefirst end electrode section 162. A conductor 119 runs from theconnection 161 to the connection 123 at the center electrode section 124of the electrode sheet 120 and to the connection 165 at the second end108 to the second end electrode section 166 of the electrode sheet 160.In this embodiment, the conductor 119 is suitably a wire running fromthe end 108 to the end 106 of the recurve actuator 105. This permits theV_(c) conductor 103 to be suitably connected to the recurve actuator 105on the first end 106 of the recurve actuator 105.

As shown in FIG. 6B, the electrical connections 121, 141, and 161suitably do not overlap. Similarly, the electrode connections 123 and163 in the center 107 suitably do not overlap. Likewise, the electrodeconnections 125, 145, and 165 at the second end 108 suitably do notoverlap. Because the referenced connections do not overlap and thus donot short to each other, the electrical connections suitably may bethrough-rivets. It will be appreciated that any suitable electrodesection connection or configuration end type may be utilized for therecurve actuator 105, including the alternate connections described inconnection with FIG. 1B above. It will be appreciated that the electrodeconfigurations described in FIGS. 6A and 6B when driven by voltagesV_(a), V_(b), and V_(c) produce alternating charge potentials across theelectrostrictive layers of the recurve actuator 105.

FIG. 6C is a side view symbolic diagram of the electrode sections ofelectrode sheets 120, 140, and 160 and the voltages applied to theelectrode sections and adjacent segments of the electrostrictive layers112 and 116. The intermediate electrode sheet 140 contains a first endelectrode section 142 and a second end electrode section 144; they areboth driven at a voltage V_(b). Adjacent to the intermediate electrodesheet 140 on one side is the electrostrictive layer 112. Adjacent theelectrostrictive layer 112 and across the electrostrictive layer 112from the intermediate electrode sheet 140 is the second electrode sheet120. The electrode sheet 120 is driven in three sections—a first endelectrode section 122, a center electrode section 124, and a second endelectrode section 126. The first end electrode section 122 and thesecond end electrode section 126 are driven at a voltage equal to V_(a).The center electrode section 124 is driven at a voltage equal to V_(c).In this embodiment, the lengths 185 of the first end electrode section122 and the second end electrode section 126 are equalized with eachother and around half as long as the length of the center electrodesection 124 (which has a center length 187). As will be described belowin connection with FIGS. 7A, 7B, and 7C, by way of example but notlimitation, arranging the two end electrode sections 122 and 126 inequal lengths, with lengths 185 equal to half of the length 187advantageously permits the recurve actuator 105, when activated, todeflect in a recurve or a half clam-shell shape, thereby maintaining theends 106 and 108 in parallel and in the same plane.

On the opposite side of the electrode sheet 140 from the layer 112 is anelectrostrictive layer 116. Adjacent to the electrostrictive layer 116,and across layer 116 from the intermediate electrode sheet 140 is theelectrode sheet 160. Like electrode sheet 120, the electrode sheet 160is divided into 3 sections—a first end electrode section 162, a centerelectrode section 164, and a second end electrode section 166. The endelectrode sections 162 and 164 are driven at a voltage equal to V_(c)while the central section 164 is driven at a voltage equal to V_(a).Also, like electrode sheet 120, the end electrode sections 162 and 166are of equalized length 185 of around one-half the length 187 of thecenter electrode section 164. With the entire intermediate electrodesheet 140 suitably driven at a variable voltage of V_(b), it will beappreciated that the electrostrictive layers 112 and 116 experience anelectrical field with a voltage potential equal to the voltagedifference between V_(a) and V_(b) for the segments of theelectrostrictive layers in segments adjoining the sections of theelectrode sheet 120 and the electrode sheet 160 driven at V_(a). Theelectrostrictive layers 112 and 116 also experience an electrical fieldwith a voltage potential equal to the difference between V_(b) and V_(c)in the segments adjoining the sections of the electrode sheets 120 and160 driven at V_(c). Thus, the first electrostrictive layer 112 issubject to an electrical field with a voltage equal to V_(ab) in the endsegments 182 and 186.

The center segment 184 of electrostrictive layer 112 is subject to anelectrical field of the voltage equal to V_(bc) where it adjoins thecenter electrode section 124 of electrode sheet 120, which is driven atV_(c). Because the center electrode section 124 of electrode sheet 120has a length 187 that is around twice as long as the length 185 of theend electrode sections 126 and 122, the end segments 182 and 186 ofelectrostrictive layer 112 subject to an electrical field of V_(ab) arehalf as long as the central segment 184 subject to an electrical fieldof V_(bc). Conversely, on the opposite side of the intermediateelectrode sheet 140, the end electrode sections 162 and 166 are drivenat a voltage of V_(c), while the central section 164 is driven at avoltage of V_(a). Thus, the second electrostrictive layer 116 is subjectto an electrical field with a voltage potential of the V_(bc) on its twoend segments 192 and 196, and a voltage potential of V_(ab) in itscenter segment 194. Because the lengths 185 of the two end electrodesections 162 and 166 are equalized, and are around half the length 187of the center electrode section 164, the end segments 192 and 196 thusare driven at a voltage equal to V_(bc) are equalized in length and andaround half as long as the center segment 194 driven with a voltagefield of V_(ab).

It will be appreciated that electrode sheet 120 and electrode sheet 160in cross-section as shown in FIG. 6C are mirror images of each othermirrored across the intermediate electrode sheet 140, but driven withalternate base voltages. In other words, the V_(c)-driven sections aredriven with the V_(a) and the V_(a)-driven sections are driven at V_(c).Put differently, the two end electrode sections of electrode sheet 120are driven at V_(a) while its center electrode section is driven atV_(c). Meanwhile, the two end electrode sections 162 and 166 of sheet160 are driven at V_(c), while its center electrode section is driven atV_(a).

When the recurve actuator 105 is driven with V_(a), V_(b), and V_(c) asdescribed in connection with FIGS. 1A, 1B, and 1C, above, it will beappreciated that as the voltage potential across the segments of theelectrostrictive layers driven with V_(a) are rising, the electricalpotential across those segments driven at voltage V_(c) are dropping.The recurve actuator 105 is thus three segments of bimorph actuatorssimilar to that described in FIGS. 1A and 1B placed end-to-end, withadjoining segments driven to curve in opposite directions.

As V_(ab) increases, the end segments 186 and 182 of theelectrostrictive layer 112 contract while the end segments 196 and 192of the second electrostrictive layer 116 expand. This causes theselinked end segments (the mechanical linkage between the electrostrictivelayers 112 and 116 is not shown in FIG. 6C) to cup towards theelectrostrictive layer 112 side. At the same time, the center segment184 of electrostrictive sheet 112, driven by an electrical field ofpotential V_(bc), expands and the center segment 194 of the secondelectrostrictive layer 116, driven at an electrical potential of V_(ab),contracts. This causes the center segments 194 and 184 which are linkedtogether (the mechanical linkage between layers 116 and 112 are notshown in FIG. 6C) to cup or curve with an inside of the curve toward thesection electrostrictive layer 116 side. The result is a recurve shape,or a half clam-shell with the two end electrode sections curving in theopposite direction from the central and longer center electrode section.When V_(ab) decreases and V_(bc) decreases the converse occurs. That is,the end segments 186 and 196, and 182 and 192, respectively, cup orcurve with the inside of the curve towards the second electrostrictivelayer 116. At the same time, the central segment made of segments 184and 194 of the electrostrictive layer 112 and the electrostrictive layer116 respectively cup towards, or curve with the inside of the curvetowards, the electrostrictive layer 112. The result is a half clamshellor recurve shape with an opposite deflection from that when V_(ab) isgreater than V_(bc).

The deflection of the recurve actuator 105 when V_(ab) and V_(bc) varieswith the variation in V_(b) as shown in FIGS. 7A, 7B, and 7C. FIG. 7Ashows the recurve actuator 105 when V_(ab) equals V_(bc). When V_(ab)equals V_(bc), the recurve actuator 105 is straight. As V_(ab) increasesand V_(bc) correspondingly decreases, as shown in FIG. 7B, the recurvedeflects in a clam-shell curve with the middle 107 deflecting and theends 106 and 108 remaining parallel. Conversely, when V_(ab) decreasesand V_(bc) increases, the center 107 deflects in an opposite directionwith the ends 106 and 108 remaining parallel as shown in FIG. 7C.

In FIG. 7A, the first end 106 and the second end 108 are connected toattachments 104 which hold the ends. As in FIGS. 6A, 6B, and 6C, therecurve actuator 105 is suitably a 5-layer sandwich with theintermediate electrode sheet 140 in the middle with the electrostrictivelayer 112 and the electrode sheet 120 on one side of the intermediateelectrode sheet 140, and the second electrostrictive layer 116 and thethird electrode sheet 160 on the other side of the electrode sheet 140.At the first end 106, the second electrode sheet 120 has a first endelectrode section 122 driven at a voltage equal to V_(a). The middlesection 124 of the second electrode sheet 120 is driven at a voltageequal to V_(c). The second end electrode section 126 of the secondelectrode sheet 120 is also driven at a voltage equal to V_(a). Theintermediate electrode sheet 140 consists of a first end electrodesection 142 and a second end electrode section 144. Both sections 142and 144 are driven at a voltage equal to V_(b). Thus, the entireintermediate electrode sheet 140 is driven at a voltage equal to V_(b).The third electrode sheet 160 has three sections like sheet 120. Itsfirst end electrode section 162 at the end 106 is driven at a voltageequal to V_(c). Its center electrode section 194 is driven at a voltageequal to V_(a). The second end electrode section 166 is driven at avoltage equal to V_(c).

The pattern of electrodes and corresponding electrical fields placed onthe first electrostrictive sheet 112 and second electrostrictive 116 inFIG. 7A, as well as FIGS. 7B and 7C as described below, is suitably thesame as symbolically shown in FIG. 6C. In FIG. 7A, the end electrodesections 122 and 126 are around half as long as the center electrodesection 124 of the second electrode sheet 120. Similarly, the two endelectrode sections 162 and 166 of the third electrode sheet 160 arearound half as long as the center electrode section 124. The endelectrode sections of the second and third electrode sheets 120 and 160are around half as long as their center electrode sections and areequalized to each other. As a result, when the center segments curve inone direction and the end segments curve in the opposite direction atthe same radius of curve, the ends 106 and 108 remain parallel. Further,driving the recurve actuator 105 in this fashion, with its first endsegment curving one way and its middle segment of around twice thelength of the end segments curving the other way, and a second endsegment curving back, suitably results in all of the layers of therecurve actuator 105 having the same total length from end 106 to end108, resulting in no sheer between the electrode sheets andelectrostrictive layers of the recurve actuator 105 at the ends 106 and108. Thus, the ends of the recurve actuator 105 can be held by theattachments 104 at the ends 106 and 108 that pin all the layers of therecurve actuator 105 together. Similarly, there is no sheer between thelayers of the recurve actuator 105 at the center 107 of the recurvebecause the recurve actuator 105 when activated has equivalent s-curvestowards each end 106 and 108 symmetrically around the center 107.

FIG. 7B shows the recurve actuator 105 when activated with V_(ab)greater than V_(bc). The electrode sheets 120, 140, and 160, attachments104, ends 106 and 108, and center electrode section 107 are as describedin connection with FIG. 7A. When V_(ac) is greater than V_(bc), portionsof the electrostrictive layers 112 and 116 between electrode sectionsdriven at a voltage equal to V_(a) and V_(b) are shorter than thosebetween electrode sections driven at voltages equal to V_(b) and V_(c).In FIG. 7A, this causes the end segments of the recurve actuator 105 tocurve towards the first electrostrictive layer 112 and the middlesegment 107 of the recurve actuator 105 to curve in the oppositedirection towards the second electrostrictive sheet 116. This results ina deflection 118 of the middle 107 equal to +Δ. As shown in FIG. 7B, thecenter segment of the recurve actuator 105 is around twice as long aseach of the end segments of the recurve. Thus, the center segment curvesin one direction the end electrode sections curves in the other. Thisforms a recurve or half clam-shell shape while the ends 106 and 108remain parallel.

It will be appreciated that a recurve actuator 105 need not be generallyone-dimensional, in other words deflecting simply along its length. Therecurve actuator 105 may be suitably disc or diaphragm-shaped, or crossor multi-pointed asterisk shaped. In such embodiments, the deflection118 when V_(ab) is greater than V_(bc) would be in cross-section thesame as shown in FIG. 7B. However, the actuator suitably would developgreater deflecting force or would apply deflection force across a widerarea.

FIG. 7C is the converse of FIG. 7B. In FIG. 7C, the recurve actuator 105is driven with V_(ab) less than V_(bc). The result is a deflection 118equal to −Δ in the opposite direction from that shown in FIG. 7B. InFIG. 7C, the ends 104 and 106 of the recurve actuator 105 with V_(ab)less than V_(bc) cup towards, or curve with the lower radius towards,the second electrostrictive layer 116, while the center 107 segment cupsor curves toward the first electrostrictive layer 112. The electrodesheets, segments, layers, ends and attachments of the recurve actuator105 in FIG. 7C are the same as described in connection with FIG. 7A.When driven with V_(ab) less than V_(bc), the recurve actuator 105assumes a recurve shape or half clam-shell opposite from that whenV_(ab) is greater than V_(bc).

FIG. 8A shows an exemplary embodiment of electrode sheets of anexemplary recurve actuator system 105. The electrode sheets 120, 140,and 160 are suitably sheet electrodes, and are shown in assembled topview with the second electrode sheet 120 above the intermediateelectrode sheet 140, both of which in turn are above the third electrodesheet 160. The electrostrictive layers 112 and 116 are not shown.

All of the connections to the sections of the electrode sheets are atthe first end 106, the second end 108, and the center 107 of theelectrode sheets 120, 140 and 160. Each electrode sheet 120, 140 and 160has a tab, 131, 151, and 171, respectively, at the end 106, and a tab133, 153, and 173, respectively, at end 108. Each tab is a projectionfrom the electrode sheet at the ends 106 and 108, respectively, witheach tab having an electrical connection. The tab 131 has an electricalconnection 121 at the end 106, the tab 151 has an electrical connection141 at the end 106, and the tab 171 has an electrical connection of 161at the end 106. At the opposite second end 108, the tab 133 has anelectrical connection of 125 at end 108, tab 153 has an electricalconnection 145 at the end 108, and tab 173 has an electrical connection165 at end 108. The second electrode sheet 120 and the third electrodesheet 160 also have connections at their center 107. The connection 123is coupled to the center electrode section 124 of the electrode sheet120. The connection 163 is coupled to the center electrode section 164of third electrode sheet 160.

It will be appreciated that in this embodiment none of the electricalconnections 121, 141, 161, 125, 145, 165, 123, and 124 overlap. As notedabove, this facilitates coupling the electrical connections to theelectrode sections by allowing through-rivets or bolts to be used as theelectrical connections. At the end 106, the tab 151 is intermediate thetab 131 and the tab 171. At the end 108, the tab 153 is intermediate thetab 133 and the tab 173. In this embodiment, the tabs 153 and 151 of theelectrode sheet 140 and their respective electrical connections 145 and141 are situated on the centerline 100 of the recurve actuator 105. Thisplaces the end connection tabs 131 and 133 of second electrode sheet 120toward a first side 109 from the centerline 100, away from the tabs andconnections of the intermediate electrode sheet 140. Conversely, the endtabs 173 and 171 of electrode sheet 160 and their respective electricalconnections 165 and 161 are on the opposite or second side 111 of thecenterline 100 of the recurve actuator 105, away from the tabs 151 and153 and electrical connections 141 and 145 of the intermediate electrodesheet 140. In this embodiment the connections 123 and 163 to the centerelectrode sections of the second electrode sheet 120 and the thirdelectrode sheet 160, respectively, are located at the center 107 of therecurve actuator 105 on opposite sides of the centerline 100 from eachother. In this exemplary embodiment, the electrical connection 123 tothe center electrode section 124, is towards the second side 111 of therecurve actuator 105 at the center 107, while the end connections 121and 125 are towards the first side 109 at their respective ends 106 and108.

The connections to the third electrode sheet 160 are a mirror image ofthe second electrode sheet 120, mirrored across the centerline 100 ofthe recurve actuator 105. The center connection 163 is towards the firstside 109 from the centerline 100 of the recurve actuator 105 at thecenter 107. The end connections 161 and 165 are towards the second side111 at their respective ends 106 and 108.

In this embodiment, the intermediate electrode sheet 140 includes afirst end electrode section 142 and a second end electrode section 144driven from their first end 106 and second end 108, respectively. Inthis assembled top view, the first end electrode section 142 and thesecond end electrode section 144 are visible through gaps 129 in thesecond electrode sheet 120 between the first electrode section 122 andthe center electrode section 124, and between the center electrodesection 124 and second end electrode section 126, respectively. It willbe appreciated that the electrode connections 123 and 163 to thesections 124 and 164, respectively, do not overlap the electrodesections 142 and 144 of the intermediate electrode sheet 140. Insteadthere is advantageously a gap (not shown) between the two sections 142and 144 of the intermediate electrode sheet 140.

FIG. 8B is a disassembled view of the three individual electrode sheets120, 140, and 160 of the recurve actuator 105. The upper electrode sheetin FIG. 8B is the second electrode sheet 120. The middle electrode sheetin FIG. 8B is the intermediate electrode sheet 140. The bottom electrodesheet in FIG. 8B is the third electrode sheet 160.

The electrode sheet 120 includes the first end electrode section 122 atthe first end 106, the center electrode section 124 at the center 107,and the second end electrode section 126 at the end 108. The first endelectrode section 122 is separated from the center electrode section 124by a gap 129. The center electrode section 124 is separated from thesecond end electrode section 126 by a gap 129.

The first section 122 is of equalized length to the second end electrodesection 126. Both in turn are around half the length of the centerelectrode section 124. In FIG. 8B, the same ratio applies to the endsections and center section of the third electrode sheet 160, describedbelow.

The first end electrode section 122 has a connection tab 121 with anelectrical connection 131 at the end 106. The first end connection tab131 and first end connection 131 on the first side 109 of centerline 100of the recurve at first end 106. The second end connection tab 123 atthe other end of the second electrode sheet 120 is on the same firstside 109 of the centerline 100 at the end 108. The second end connectiontab 123 to the second end electrode section 126 has an electricalconnection 125.

The center electrode section 124 has a notch 127 at its center 107 onthe first side 109 so that the center electrode section 124 does notoverlap the center electrode connection 163, on the third electrodesheet 160. The notch 127 extends around two-thirds of the way from thefirst side 109 of electrode sheet 120 towards the second side 111. Thenotch may be of any suitable width or shape so that the center electrodesection 124 of second electrode sheet 120 does not overlap the centerconnection 163 to the third electrode sheet 160 situated below theintermediate electrode sheet 140 from the second electrode sheet 120when the electrode sheets are assembled together. In alignment with thenotch 127 at the center 107, but not within the notch 127 itself, is thecenter connection 123 to the center electrode section 124. The centerconnection 123 is thus towards the second side 111 of the centerelectrode section 124 (the notch 127 is towards the first side 109). Thecenter electrode connection 123 is located towards the second side 111so that it falls within a notch 167 in the center electrode section 164of the third electrode sheet 160, when the electrode sheets areassembled. The notch 167 has the same function as the notch 127 insecond electrode sheet 120. This advantageously prevents the centerelectrode section 164 of the third electrode sheet 160 from overlappingthe center electrode connection 123 to the center electrode section 124of the second electrode sheet 120.

The intermediate electrode sheet 140 (the center electrode sheet in FIG.8B), has a first end electrode section 142 at the end 106 and a secondend electrode section 144 at end 108. The two sections are divided by acenter gap 149. The first end electrode section 142 has a connection tab151 with an electrical connection 141. The connection tab 151 and theelectrical connection 141 are situated on the centerline 100 of therecurve actuator 100. The connection tab 151 at the end 106 of theintermediate electrode sheet 140 has two edges 156 on opposite sides ofthe centerline 100 from the electrical connection 141. The connectiontabs 131 and 171 are arranged away from the center line 100 of therecurve actuator 105 from these edges so that the tabs 131, 151, and 171do not overlap. Tabs 131 and 171 are thus arranged on opposite edges 156of the tab 151 at the end 106. A similar arrangement of tabs is at theopposite end 108 electrode sheets. A second end tab 153 is linked to thesecond end electrode section 144 of the intermediate electrode sheet140. The tab 153 has an electrical connection 145, and both the tab 153and the connection 145 are on the centerline 100 at the end 108. The tab153, similar to the tab 151, has two edges 156 on opposite sides of thecenterline 100 from the electrical connection 145. The tabs 133 and 173on end 108 are arranged on opposite sides of the center line 100 outsideof the edges 156 of the tab 153. As a result, the tabs 133, 153, and173, and their accompanying electrical connections 125, 145, and 165,respectively, do not overlap at end 108.

The third electrode sheet 160 is a mirror image of the second electrodesheet 120 mirrored across the centerline 100. The third electrode sheethas a first section 162 at the end 106, a center electrode section 164at the center 107, and a second end electrode section 166 at the end108. The first end electrode section 162 is separated from the centerelectrode section 164 by a gap 129. The center electrode section 164 isseparated from the second end electrode section 166 by another gap 129.The first end electrode section 162 has a connection tab 171 with anelectrical connection 161 at the end 106. The first end connection tab171 of the third electrode sheet 160 is located towards the second side111 of the centerline 100 at the end 106. The second end connection tab173 is located towards the same second side 111 at the opposite secondend 108. The second end electrode tab 173 at the end 108 has anelectrical connection 165. As noted above, arranging the end connections171 and 173 towards the second side 111 prevents them from overlappingand thus shorting out to the end connections 131 and 133 which aresituated towards the first side 109, or across the center line 100 ofthe recurve.

The center electrode section 164 has a center connection 163 located atthe center 107. It will be appreciated that when the second electrodesheet 120, intermediate electrode sheet 140, and third electrode sheet160 are stacked, the center electrical connection 163 to the centerelectrode section 164 falls within the center gap 149 of theintermediate electrode sheet 140, and the notch 127 in the first side109 of the second electrode sheet 120. Therefore, the center connection163 does not overlap with, or short out to, any of the electrodesections or connections on the intermediate electrode sheet 140 or thesecond electrode sheet 120. Put differently, the center electricalconnection 163 on the center electrode section 164 of the thirdelectrode sheet 160 at the center 107 is located towards the first side109 of the recurve actuator 104. This is the same side that defines thenotch 127 in the second electrode sheet 120.

The center electrode section 164 of the third electrode sheet 160 alsodefines a center notch 167 to prevent the center electrode section 164from overlapping and thus shorting to the center electrode connection123. In this example, the notch 167 is a mirror image of notch 127. Thenotch 197 in this exemplary embodiment extends approximately two-thirdsof the way across the center electrode section 164 from the second side111 toward the first side 109.

Summarizing FIG. 8B, the second electrode sheet 120 has end connectiontabs 133 and 131 on the first side 109 of the recurve actuator 105 whilehaving its center connection 123 on the opposite, or second side 111 ofthe recurve actuator 105. The end connection tabs 171 and 173 on thirdelectrode sheet 160 are the converse of this, and are thus situated onthe second side 111 of the recurve actuator 105, while the centerconnection 163 of the third electrode sheet 160 is on the first side 109of the recurve actuator 105. The second electrode sheet 120 notch 127extends in from the first side 109 at the center 107, while the notch167 in the center electrode section 164 of the third electrode sheet 160extends in from the second side 111. As noted above, the electrode sheet120 is a mirror image of third electrode sheet 160 across the centerline100. For manufacturing purposes, this mirror imaging is advantageouslyaccomplished by simply flipping or rotating the electrode sheet 120 by180 degrees around the centerline 100 of the recurve actuator 105. Thus,the second electrode sheet 140 is suitably the same as the thirdelectrode sheet 160 for manufacturing purposes.

A bridge connection between the first end electrode section 142 and thesecond end electrode section 144 of the intermediate electrode sheet 140suitably could be arranged along the center line 100 of the intermediateelectrode sheet 140. Such a bridge connection may connect the twosections 142 and 144 without overlapping or shorting to the centerelectrode connections 123 and 163. This is because the notches 167 and127 in this embodiment extend approximately two-thirds the way acrosstheir respective electrode sheets 160 and 120. Such a bridge wouldpermit the intermediate electrode sheet 140 to be driven from either end106 or 108 without the necessity of driving both ends with a voltageequal to V_(b).

As with the arrangement of connections in the bimorph actuator describedin FIG. 1A and FIG. 1B above, any suitable alignment of electrodeconnections, tab shapes, and tab connections may be utilized to provideto provide appropriate voltages to the electrode sections 122, 124, 142,144, 162, 164, and 166.

As shown in FIGS. 9A and 9B, it will be appreciated that multiplerecurve actuators may be arranged in an array to increase the totaldeflection available for driving mechanical devices and other equipment.FIGS. 9A and 9B are cross-sections of an array 205 of two recurveelements 207 and 209 arranged to create a deflection 218 that is aboutdouble the deflection from that obtained from a single recurve array. InFIG. 9A, a first recurve actuator 207 is a recurve actuator similar tothat described in FIGS. 6, 7 and 8 above, or a multi-layer recurveactuator as described in connection with FIGS. 10 and 11 below. Theactuator 207 is attached at its center 227 to a device 220 to be movedor deflected. The first element 207 has a first end connection 206 and asecond end connection 208 both of which are connected to a secondrecurve element 209. The first end connection 206 and the second endconnection 208 are arranged so that the first recurve element 207 andthe second recurve element 209 clear each other sufficiently so thatboth may deflect their full range in both directions as the voltagesapplied to the first and second elements 207 and 209 vary. By way ofexample, but not limitation, the end connections 206 and 208 suitablymay include spacers to provide clearance between the two recurveelements 207 and 209

The ends of the second recurve element 209 connect at the first endconnection 206 to the first element 207 and at the second end connection208 to the opposite end of first element 207. The center 217 of thesecond element 209 is attached to a base 210. In summary, the array 205is thus connected to a base 210 at the middle of the second element 209and is connected to the device 220 being driven at the center 227 of thefirst element 207, with the two elements 207 and 209 connected at theirrespective ends by end connectors 206 and 208. The two end connections206 and 208 in this exemplary embodiment are free to move as the arrayis actuated, but the end connections may be attached or stabilized inother embodiments.

The array 205 generates deflection of the device 220 being driven byactuating the two recurve elements 207 and 209 in opposite directions.This causes the centers 207 and 217 of the two arrays to open to deflectaway from each other when the array 205 is expanded, as in FIG. 9A, andthe centers 207 and 217 to contract or retract toward each other whenthe array 205 is retracted, as in FIG. 9B. By driving the first element207 opposite from the second element 209, the total deflection 218 ofthe array 205 equals around twice that of either of the elements 207 or209 alone. The mechanical device 220 being driven thus is pushed awayfrom the base 210 when the array 205 extends, and the device 220 ispulled toward the base 210 when the array contracts. The net deflection218 of the array 205 thus equals around 2Δ, where Δ is the amount ofdeflection obtainable by a single recurve actuator. It will beappreciated that if the two elements 207 and 209 are driven at aresonant frequency that the deflection 218 may be larger than if thearray 205 is driven at a frequency that is not resonant. It will beappreciated that recurve arrays such as the array 205 shown in FIGS. 9Aand 9B may be connected in series or in parallel with other actuators toobtain either further increased deflection or increased force ofdeflection.

It will also be appreciated that FIGS. 9A and 9B are side views ofrecurve actuator arrays that have a generally one-dimensional(length>>width) rectangular configuration similar to that described inFIGS. 6, 7, and 8. Thus, it will be appreciated that two-dimensional, asopposed to generally one-dimensional, arrays are possible utilizingtwo-dimensional recurves such as wide (width>>length), disc-shaped(circular), cross-shaped (such as a “red cross” shaped cross), ormulti-pointed asterisk or star-shaped recurve actuators driven withtheir center segments curving in opposite directions from their end oredge segments. It will also be appreciated that recurve actuators, aswell as arrays based on such actuators, may be extended laterally. Thisresults in actuators or arrays that are wide and short, as opposed tonarrow and long. Similarly, arrays may overlap or be mechanicallyattached in any suitable fashion to obtain either increased force to beapplied to the device being driven or increased deflection.

It will be appreciated that the force that can be derived from a recurveactuator can be increased by increasing the number of electrostrictivelayers in the actuator. FIGS. 10A and 10B provide exploded and symbolicviews, respectively, of an exemplary multi-layer recurve actuator of thepresent invention. FIG. 10A is an exploded perspective side view of asix layer recurve actuator 350 with six layer units 300, 302, and 304above a central reference plane 305, and three layer units 306, 308, and310 below the reference plane 305. Each of the layer units 300, 302,304, 306, 308, and 310 includes electrode sections that drive a sheet ofelectrostrictive material 112 incorporated in each layer. In thisembodiment, each of the layer units 300, 302, 304, 306, 308, and 310includes a sandwich of an intermediate electrode sheet 140, a sheet ofelectrostrictive material 112, and second electrode sheet 120. Eachlayer has the same component sheets, but is oriented differently in themulti-layer stack that forms the multi-layer recurve actuator 350.

Returning to FIG. 8B it will be appreciated that the third electrodesheet 160 is a mirror image or a rotation along the center line 100 ofthe second electrode sheet 120. Thus, it will further be appreciatedthat a three layer sandwich of the intermediate electrode sheet 140, theelectrostrictive sheet 112, and the second electrostrictive sheet 120,in that order respectively, is identical to, albeit rotated 180 degreesaround the centerline 100, a sandwich of the intermediate electrodesheet 140, the electrostrictive sheet 112, and the third electrode sheet160. This same three layer sandwich is included in each of the layerunits 300, 302, 304, 306, 308, and 310 of the multi-layer recurveactuator 350 in FIG. 10A, albeit rotated in different orientations.

FIG. 10A thus is an exploded isometric view of the six layers of themulti-layer recurve actuator 350. The center reference plane 305 forms acenter reference plane defining the orthogonal x-axis 321 (right to leftin FIG. 10A) and y-axis 324 (towards the viewer and away from the viewerin perspective in FIG. 10A). In this exemplary embodiment all of thelayer units 300, 302, 304, 306, 308, and 310 are rectangular and ofequal size. They are longer in the x direction than they are wide in they direction. All layers are aligned with their lengths 351 in the x-axis321. The layers have their midpoints 352 centered at the origin of thex-axis 321/y-axis 324. The layers are stacked above and below thereference plane 305 with their midpoints 352 along the orthogonal z-axis323 (up and down in FIG. 10A), directly above 320 or below 330 thex-axis 321/y-axis 324 origin. Layer units 304, 302, and 300 are locatedabove 320 the reference plane 305 stacked along the z-axis 323. Layerunit 304 is closest to the reference plane 305. Moving up, layer unit302 is next, and layer unit 300, in this embodiment, is furthest above320 the reference plane 305. Below 340 the reference plane 305 are layerunits 306, 308, and 310 centered on the z-axis 323 at increasingdistance from the reference plane 305, respectively. When assembled, allthe layer units 300, 302, 304, 306, 308, and 310 are stacked immediatelyadjoining the neighboring layer. The multi-layer recurve actuator 350thus has six sheets of electrostrictive material 112. Eachelectrostrictive sheet 112 is sandwiched between a pair of electrodesheets 120 and 140. Not shown in FIG. 10A are the attachment orattachments between the layer units 300, 302, 304, 306, 308, and 310. Ina presently preferred embodiment, the attachments are double-stick mylarsheets between the layers. However, any suitable method of attachmentmay be utilized, including without limitation the methods described inconnection with FIG. 1A above. Each electrode sheet 120 has a centerelectrode section 124 and two end electrode sections 122 and 126. Eachintermediate electrode sheet 140 has two electrode sections 144 and 142.The electrode sections may be driven by any appropriate configuration ofconnections and attachments. In the embodiment shown in FIG. 10A, theconnections are as shown on the corresponding electrode sheets 140 and120 in FIG. 8B above.

It will be appreciated that to form a recurve shape or a half clam-shellshape, the ends of the electrostrictive material 112 in the end segments360 of the layer units 300, 302, 304 above the reference plane 305 aredriven in an opposite sense from the end segments 360 in the layer units306 308 and 310 below the reference plane 305. Similarly, the centersegments 361 of the layer units 300, 302, and 304 above the referenceplane 305 are driven opposite their respective end segments 360, andalso opposite the center segments 361 of the layer units 306, 308, and310 below the reference plane 305. It will be appreciated that thereferences herein to below and above the reference plane 305 are fordescriptive purposes only, and the multi-layer recurve array 350 may beoriented at any angle appropriate to the device being driven by theactuator.

In this embodiment, the two sections 142 and 144 of the intermediateelectrode sheet 140 in every layer unit are driven at a voltage equal toV_(b). This is true for all the layer units 300, 302, 304, 306, 308, and310. Above the reference plane 305, the end electrode sections 122 and126 of the second electrode sheets 120 of layer units 300, 302, and 304are driven with a voltage equal to V_(a). The center electrode sections124 of second electrode sheets 120 of the layer units 300, 302 and 304above the reference plane 305, are driven with a voltage V_(c). In FIG.10A, as in FIG. 8B, the end electrode sections 122 and 126 of electrodesheets 120 are equalized in length and around one half of the length ofthe center electrode section 124. Thus, the end one-quarters, or endsegments 360, of the electrostrictive sheet 112 in each layer unit 300,302, and 304 experience an electrical field with a potential of V_(ab),while the center two-quarters, or center segments 361, of eachelectrostrictive sheet 112 above the reference plane 305 experience anelectrical field with a voltage potential of V_(bc).

Conversely, below the reference plane 305, the end electrode sections126 and 122 of each of the layer units 306, 308, and 310 are driven at avoltage equal to V_(c), while their respective center electrode sections124 are driven at a voltage V_(a). The same as above the reference plane305, the end electrode sections 122 and 126 of layer units 306, 308, and310 below the reference plane 305 are equalized in length, and arearound half the length of the center electrode sections 124. Thus, bothend one-quarters, or end segments 360, of the electrostrictive material112 in each of the layer units 306, 308, and 310 experience anelectrical field of voltage potential V_(bc), while their centertwo-quarters, or center segments 361 experience an electrical field ofvoltage potential V_(ab).

This is shown symbolically in FIG. 10B. The multi-layer recurve actuator350 has three layer units 300, 302, and 304 above the reference plane305 and three layer units 306, 308, and 312 below the reference plane305. The electrode sections driven by V_(a) are symbolically denoted“A,” the electrode sections driven by V_(b) are symbolically denoted“B,” and the electrode sections driven with voltage equal to V_(c) aredenoted “C”. Starting at the reference plane 305 and moving up throughlayer units 304, 302, and 300 sequentially, nine components areencountered—three in each of the three layers above the reference plane305. Moving above the reference plane 305, first is the intermediateelectrode sheet 140 of layer unit 304, with both electrode sections 142and 144 driven at a voltage equal to V_(b). Second is a sheet ofelectrostrictive material 112 of layer unit 304. Third is the secondelectrode sheet 120 of layer unit 304 with its end electrode sections122 and 126 driven at a voltage equal to V_(a) and with its a centerelectrode section 124 driven at a voltage of V_(c). Fourth, above layerunit 304 is layer unit 302 with the second electrode sheet 120, with itsend electrode sections 122 and 126 driven at a voltage equal to V_(a),and its center electrode section 124 driven at a voltage equal to V_(c).Fifth is the electrostrictive material sheet 112 of layer unit 302.Sixth is the intermediate electrode sheet 140 of layer unit 302 drivenat a voltage equal to V_(b) in both of its electrode sections 142 and144. Above layer unit 302 is layer unit 300, and thus seventh is anintermediate electrode sheet 140 with its two electrode sections 144 and142 both driven at a voltage equal to V_(b). Eighth is theelectrostrictive sheet 112 of the layer unit 300. Ninth, and last inthis exemplary embodiment, is the second electrode sheet 120 of layerunit 300 with its end electrode sections 120 sections 126 and 122 drivenat a voltage of V_(a) and its center electrode section driven at avoltage equal to equal to V_(c). The layering of the same ninecomponents occurs in the same sequence in layer units 306, 308, and 310,below the reference plane 305, starting at the reference plane 305 andmoving down, but with the end electrode sections 126 and 122 driven at avoltage equal to V_(c), and with the center electrode sections 124driven at a voltage equal to V_(a).

It will be appreciated that adjoining layers, such as layer units 304and 302, have their adjoining electrode sheets being the same. In thisexample, adjoining electrode sheets of the layer units 304 and 302 areboth second electrode sheets 120 driven with a voltage V_(a) in theirend electrode sections 122 and 126, and a voltage of V_(c) in theirmiddle electrode sections 124. As a result, when the layers are stackedin this manner, adjoining electrode sheets of adjoining layers (whichhave no electrostrictive material 112 between them) have the sameapplied voltages in their respective end and center electrode sections.Thus there is no voltage leakage or field formed between the layerunits. This is true throughout the stack of the multi-layer recurveactuator 350. The layers are all oriented so that intermediate electrodesheets 140 of the respective layers abut intermediate electrode sheets140 of adjoining layers, while the second electrode sheets 120 of therespective layers adjoin second electrode sheets 120 of the adjoininglayers. The intermediate electrode sheets 140 of layer units 304 and 306abut each other at the reference plane 305.

Reviewing the internal symmetry of the stack of the multi-layer recurveactuator 350 in FIG. 10B, it will be appreciated that layer units 304and 300 are identically oriented, while the intermediate layer unit 302is the same as layer units 304 and 300 but inverted around itselectrostrictive layer 112. Similarly, the layer units 306 and 310 belowthe reference plane 305 are identically oriented while the intermediatelayer unit 308 is inverted around its electrostrictive layer 112. Fromthe symmetry of FIG. 10B, the electrode sheets immediately adjoining thereference plane 305 are both intermediate electrode sheets 140, with alltheir sections 142 and 144 driven at a voltage equal to V_(b). Infunction, therefore, it will be appreciated that the layer units 304 and306 adjoining each other across the reference plane 305 encompass twoelectrostrictive layers 112 with electrode sheets 140 between themdriven at a voltage equal to V_(b), and second electrode sheets 120outside of them driven with their ends at opposite voltage potentialsV_(a) and V_(c), respectively, and their center electrode sectionsdriven at opposite voltage potentials V_(c) and V_(a), respectively.This forms functionally the same recurve configuration as in FIG. 6C.The remaining layer units 302 and 300 above the reference plane 305 andlayer units 308 and 310 below the reference plane 305 strengthen and adddeflective force to the recurve. As a result, the multi-layer recurveactuator 350 deflects in the same manner as shown in FIGS. 7A, 7B and7C, but with additional deflecting force.

Returning to FIG. 10A, layer units 302 and 308 functionally remain thesame when placed into the stack inverted from their adjoining layerunits 300 and 304, and 306 and 310, respectively. In other words, theirend segments 360 of electrostrictive material 112 are subject to thesame electric charge as the adjoining layers (V_(a) for layer units 300,302 and 304, and V_(c) for layer units 306, 308 and 310). It will beappreciated, however, that inverting the layer unit 304 around thex-axis 321 to form the layer unit 302 without a second rotation resultsin an overlap of electrode connections when the multi-layer recurveactuator 350 is connected to its power source. However, if the layerunit 304 is rotated 180 degrees around its x-axis (i.e., inverted aroundits electrostrictive sheet 112) and then spun 180 degrees around itsz-axis 323 to form the layer unit 302, the electrical connections of thesecond electrode sheet 120 of the layer units 302 and 304 areadvantageously aligned (not shown—shown in detail in FIG. 11).

Assembly of the multi-layer recurve actuator 350 utilizing identicallayer units as shown in FIG. 10A, from furthest above 320 the referenceplane 305 to furthest below 330 the reference plane 305 with the sixlayer units thus starts with layer unit 300. Layer unit 302 is identicalto layer unit 300 but rotated 180 degrees around its length 351 orx-axis 321 and spun 180 degrees along its vertical or z-axis 323. Layerunit 304 is oriented the same as layer unit 300. Below the referenceplane 305, layer unit 306 is identical to layer unit 300 rotated 180degrees on its longitudinal or x-axis 321. Layer unit 308 is identicalto layer unit 300, but rotated 180 degrees on its vertical or z-axis323. Layer unit 310 is oriented the same as layer unit 306, that is thesame as layer unit 300 rotated 180 degrees around its length 351 orx-axis 321.

In one presently preferred embodiment, each of the six layers areattached to its one or two neighbors with double-sided adhesive mylarsheets to form a unitary multi-layer recurve actuator 350. In theorientation shown in FIG. 10A, when V_(ab) is greater than V_(bc), thecenter of the multi-layer recurve actuator 350 curves upward, above 320the reference plane. When V_(ab) is less than V_(bc), the actuatordeflects downward, below 330 the reference plane 305. Both deflectionsform a recurve shape similar to that shown in FIGS. 7B and 7C,respectively.

FIG. 11 is an exploded isometric view of the electrode configurations ofan exemplary embodiment of a multi-layer recurve actuator 350 of thepresent invention. In this embodiment, the multi-layer recurve actuatoragain has six layer units 300, 302, 304, 306, 308 and 310. Each layerunit includes an intermediate electrode sheet 140 and a second electrodesheet 120 with an intermediate electrostrictive sheet (not shown).

Layer unit 300 furthest above the reference plane 305 includes anintermediate electrode sheet 140 and a second electrode sheet 120. Theseelectrode sheets are suitably in configured the same as the intermediateelectrode sheet 140 and the second electrode sheet 120 described in FIG.8B. The intermediate electrode sheet 140 and the second electrode sheet120 are assembled into a layer unit 300 with a layer of electrostrictivematerial (not shown) intermediate them. The layer unit 300 has a firstend 106 and a second end 108, a first side 109, and a second side 111.The layer unit 300 is rectangular, and its length 351 between its ends106 and 108 is longer than its width 353 between sides 109 and 111. InFIG. 11, the electrode sheets 120 and 140 are oriented parallel to thereference plane 305, and the ends 106 and 108 of the layer unit 300 arealigned along an x-axis 321 (right to left in FIG. 11), with theirmidpoint centered on a vertical axis or z-axis 323 (up or above and downor below in FIG. 11). In layer unit 300, the second electrode sheet 120is above 320 the intermediate electrode sheet 140. Second electrodesheet 120 has a connection tab 131 on its first end electrode section122 at the first end 106 (to the right in FIG. 11). Second electrodesheet 120 has a second end connection tab 133 at the second end 108 (tothe left in FIG. 11). Both the first end connection tab 131 and thesecond end connection tab 133 are located towards the first side 109 ofthe second electrode sheet 120 from the center line or x-axis 321 of thesecond electrode sheet 120 (in perspective, away from the viewer fromthe x-axis 321 in FIG. 11).

As in FIG. 10A, the lengths of the end electrode sections 126 and 122are equalized, and around one-half the length of the center electrodesection 124. As noted above, the center electrode section is aroundtwice as long as the two end electrode sections. This permits the endsof the recurve to remain parallel when the center electrode section isdeflected up or down.

The center electrode section 124 of the second electrode sheet 120 has acenter electrical connection 123. The center connection 123 is locatedapproximately equi-distant between the ends 106 and 108 at a center 107of the second electrode sheet 120 and towards the second side 111 of thesecond electrode sheet 120 from the centerline or x-axis 321 (inperspective, towards the viewer from the x-axis 321 in FIG. 11). Alsolocated at the center 107 of the second electrode sheet 120 is a notch127 defined in the center electrode section 124. The notch extends fromthe first side 109 of the second electrode sheet 120 at its center 107approximately two-thirds of the way towards the second side 111 of thesecond electrode sheet 120. As described above, the notch 127 allows thesecond electrode sheet 120 to be inverted and/or overlapped. As aresult, alternating center electrode sections 124 of the other layerunits can be connected without their respective V_(a) and V_(c)connections overlapping, and thus shorting out, if by way of example andnot limitation, the V_(a) and V_(c) connections are through-bolted orriveted. The first end electrode section 122 of the second electrodesheet 120 is separated from the center electrode section of the secondelectrode sheet by a gap 129. Similarly, the center electrode section124 is separated from the second end electrode section 126 by anothergap 129. In this view, the two electrode sections 142 and 144 of theunderlying intermediate electrode sheet 140 in the layer unit 300 arevisible through the gaps 129 in second electrode sheet 120. Theintermediate electrode sheet 140 of layer unit 300 has a first endelectrode section 142 and a second end electrode section 144 separatedby a gap (not shown) at the center 107. At the first end 106 of theintermediate electrode sheet 140 a connection tab 151 is located alongthe centerline or x-axis 321. The connection tab 151 has an electricalconnection 145. Similarly, on the second end 108, the intermediateelectrode sheet 140 has a connection tab 153 with an electricalconnection 145, also located along the centerline or x-axis 321. The endconnection tabs 131 and 133 of the second electrode sheet thus do notoverlap the end connection tabs 151 and 153 of the intermediateelectrode sheet 120, respectively. Further, the end connection tabs 131and 133 of the second electrode sheet 120 are arranged towards the firstside 109 of the second electrode sheet 120 in FIG. 11. In FIG. 11, thelayer unit 300 is located with its first end 106 to the right and itssecond end 108 to the left.

In this configuration, the V_(b) connection 102 to the intermediateelectrode layer 140, including both first end electrode section 142 andsecond end electrode section 144, is coupled to electrical connections145 at the centerline or x-axis 321 of the layer unit 300. The endelectrode sections 122 and 126 of the second electrode layer 120 arecoupled to the V_(a) conductor 101 by electrical connections 121 and 125respectively, at their respective electrical tabs 131 and 133 (inperspective view, towards the first side 109 back from the centerline orx-axis 321 of the layer unit 300). The center electrode section 124 ofthe second electrode sheet has its electrical connection in the center107 of the layer unit 300 along the y-axis 325, towards the second side111 (in perspective view; forward from the centerline or x-axis 321 ofthe layer unit 300). The V_(c) conductor 103 is attached to the centerelectrode section 124 of the second electrode layer 120 of layer unit300 at its connection point 123.

It will be appreciated that in the exemplary embodiment in FIG. 11, allof the intermediate electrode sheets 140 of all of the layer units 300,302, 304, 306, 308, and 310 are driven from end connection tabs at theends of the intermediate electrode sheets 140.

To recapitulate the orientation of layer unit 300, its upper electrodesheet is the second electrode sheet 140. The two end electrode sections122 and 126 being driven by a voltage V_(a) are arranged in perspectiveaway from the viewer from the x-axis or centerline 321. Electrode sheet140 has a center electrode section 124 driven at a voltage V_(c) withthe connection in perspective towards the viewer from the centerline321. These orientations are specifically noted because the balance ofthe layer units of the multi-layer recurve actuator 350 are identicallayer units to unit 300 either rotated around their x-axis 321, aroundtheir z-axis 323, or rotated around both their x and z-axes. It will beappreciated that alternative rotational moves such as rotation aroundthe y-axis 325 or other combinations of rotations can result in similarorientations.

Layer unit 302, is substantially identical to layer unit 300, but isoriented as if layer unit 300 was rotated 180 degrees around its x-axis321 and then spun 180 degrees along its z-axis 323. All of the componentreferences in layer unit 302 are the same as for layer unit 300. Byrotating layer unit 300 around its x-axis and then spinning it aroundits z-axis, the intermediate electrode sheet 140 is now above or furtheraway from the reference plane 305 in relation to the second electrodesheet 120 of layer unit 302. This rotation places the first end 106 ofthe layer unit 302 to the left and the second end 108 to the right.However, the first side 109 of layer unit 302 in perspective viewremains away from the viewer while the second side 111 remains towardsthe viewer. This is the same side-to-side configuration of layer unit300. The result is that the electrode connections 121 and 125 to the endelectrode sections 122 and 126 of the second electrode layer 120 (notvisible in Layer 302 because they are covered by the intermediateelectrode sheet 140) are arranged away from the viewer from the x-axisor centerline 321 of the layer unit 302. The connections 121 and 125 arethus in vertical alignment with connections 125 and 121 of the endelectrode sections 126 and 122 of the layer unit 300 above. Theconnection 121 for layer unit 302 to V_(a) conductor 101 is alignedbelow the V_(a) end connection 125 for layer unit 300 above, both to theleft. Similarly, connection 125 to the V_(a) conductor 101 at the secondend 108 on layer 302 is aligned under its corresponding end connection121 in the layer unit 300 above, both to the right.

The center electrode section 124 of the second electrode sheet 120 oflayer unit 302 is driven by its center connection 123. That connection123 is visible through the central gap 149 in the two electrode sections142 and 144 of the intermediate electrode sheet 140. The centralconnection point 123 of layer unit 302 is in perspective view is locatedtowards the viewer from the x-axis 321 along the y-axis 325 in verticalalignment with, or directly below, the center electrode connection 123for the layer unit 300 above. The end electrode sections 142 and 144 ofthe intermediate electrode layer 140 of layer unit 302 are both drivenfrom their respective ends 106 and 108 on connection tabs 151 and 153,respectively, with electrical connections 145 to the V_(b) conductor102, on the centerline or x-axis 321.

Layer unit 304 includes the same components and configuration as layerunit 300 and is oriented identically to layer unit 300, but is stackedbelow layer unit 302 and immediately above the reference plane 305.Oriented identically with layer unit 300, layer unit 304 has its secondelectrode sheet 120 above its intermediate electrode sheet 140. Thefirst end electrode section 142 and 144 of the intermediate electrodelayer 140 are both driven from their respective ends 106 and 108 onconnection tabs 151 and 153, respectively, with electrical connections145 to the V_(b) conductor 102. The two end electrode sections 122 and126 of the second electrode sheet 120 of layer unit 304 are driven attheir respective ends 106 and 108 through connections 121 and 125 onconnection tabs 131 and 133, respectively. Connection tab 131 to theright, and connection tab 133 to the left 333, are arranged inperspective view behind the centerline or x-axis 321 of layer unit 304.

It will be appreciated that this arrangement of layer units 300, 302,and 304 allow the center electrode sections 124 to be driven by theV_(c) conductor 103 through the center connections 123 at the center107. In addition, in all three layer units 300, 302 and 304, theconnections 123 to the V_(c) conductor 103 are, in perspective view,towards the viewer from the x-axis or centerline 321 of layer units 300,302 and 304. Conversely, the V_(a) conductors 101 are in verticalalignment behind, or away from the viewer from the x-axis 321 and thusbehind the connections 145 to the respective end electrode sections 142and 144 of the intermediate electrode sheets 140 of each of the threelayers. For this to occur, layer units 300, 302 and 304 all have theirsecond side 111 towards the viewer and their first side 109 away fromthe viewer.

Each layer unit above the reference plane 305 thus has five electricalconnections: a V_(c) conductor 103 connected to each center electrodesection 124; two V_(a) conductors 101, one at each end 106 and 108,connected to the end electrode sections 122 and 124; and two V_(b)conductors 102, one at each end 106 and 108, connected to the twoelectrode sections 142 and 144.

The layer units 306, 308, and 310 below the reference plane 305 arefurther rotations of a layer unit with the same components andconfiguration as layer unit 300. Layer units 306, 308 and 310 all havetheir first side 109 towards the viewer and their second side 111 awayfrom the viewer. Layer unit 306 has its first end 106 to the right andits second end 108 to the left. Layer unit 308 has its first end 106towards the left and its second end 108 towards the right. Layer unit310 is oriented the same as layer unit 306, with its first end 106 tothe right, and its second end 108 to the left. As in layer unit 300,layer units 306, 308, and 310 have five electrical connections each.Both end electrode sections 124 and 122 of the second electrode sheets120 of the three layers units 306, 308, and 310 below the referenceplane 305 are connected to the V_(c) conductor 103. To the left, heV_(c) conductor 103 is connected to connection 125 on tab 133 on end 108of layer unit 306, to tab 131 with connection 121 on end 106 of layerunit 308, and connection 125 on tab 133 on end 108 of layer unit 310. Tothe right, the V_(c) conductor 103 is connected to tabs on the 131 andconnection 131 at end 106 of layer unit 306, connection 125 on tab 133of end 108 on layer unit 308, and tab 131 with connection 121 on end 106of layer unit 310. The V_(c) conductor 103 connections to the tabs onthe left ends and on the right ends are all towards the viewer from thecenterline or x-axis 321 of the layer units 306, 308, and 310. This isin contrast to the end electrode sections of the second conductor sheets120 of the layer units 300, 302 and 304 above the reference plane 305which are connected to V_(a) conductor 101 away from the viewer from thecenterline or x-axis 321. Thus, the end connections to the V_(a)conductors 101 on both ends of the layer units 300, 302 and 304 abovethe reference plane 305 do not overlap with the connections to the V_(c)conductors 103 on both ends of the layer units 306, 308, and 310 belowthe reference plane 305. The connections to the V_(a) conductors 101 onthe ends of the layer units can thus be through-bolted orthrough-riveted or through-connected without shorting to the V_(c)conductors 103, and vice versa.

The center electrode section 124 of the second electrode sheet 120 ofthe three layer units 306, 308, and 310 below the reference plane 305are all connected to a V_(a) conductor 101. With the layer units 306,308, and 310 oriented as described above, these connections 123 to thecenter conductor section 124 of these three layers is located at thecenter 107 between the two ends 106 and 108 of each of the layers.Further, these connections 123 are, as viewed in perspective, away fromthe viewer from the centerline or x-axis 321. This is in contrast to theV_(c) conductor 103 connection to the center electrode sections of thethree layer units 300, 302, and 304 above the reference plane 305, whichare towards the viewer from the centerline or x-axis 321 of the unitlayers. Like the ends, it will be appreciated that the V_(a) conductor101 and the V_(c) conductor 103 can be through connected to the centerelectrode sections 124 of the three layers below the reference plane306, 308, and 310, and the three layers above the reference plane 300,302, and 304, respectively, without overlapping or shorting.

It will thus be appreciated that by manufacturing a number of layerunits in the configuration of layer unit 300, a multi-layer array 350can be assembled with a number of layer units above the center referenceplane 305, and a number of layer units below the reference plane,thereby forming a multi-layer recurve actuator 350. In this exampleembodiment there are three such layer units above the reference plane305 and three layer units below, but a lesser or greater number of layerunits may be utilized. It will be appreciated that additional layerunits add more deflection force to the multi-layer recurve actuatoruntil their combined stiffness and thickness affects the deflection ofthe actuator.

It will be appreciated that the x, y and z-axes given in FIG. 11, andthe respective directions and perspectives along and from the referenceplane 305 are for reference only. It will be appreciated that themulti-layer recurve actuator 350, like the recurve actuator described inreference to FIGS. 6A and 6B, may be of any suitable two-dimensionalshape. By way of example and not limitation, instead of a rectangularshape with a longer length along the x-axis 321 than width along they-axis 325, a multi-layer recurve actuator may be wider on the y-axis325 than it is long along the x-axis 321 thereby forming a linearactuator. Alternately, a multi-layer recurve actuator suitably may bedisc-shaped, cross-shaped, or a multi-pointed star or other outline onthe x-y plane thereby forming a multi-layer recurve that would generateadditional force to deflect with its center while maintaining the rim orends co-planar. Such actuators, by way of example and not limitation,suitably may also be assembled into multi-element arrays, with linear,cylindrical, cross or star shaped outlines. It will be appreciated thatthe multi-layer recurve actuator and recurve actuator arrays of thepresent invention may be utilized to drive a wide variety of devices andequipment.

FIGS. 12A, 12B, and 12C show the operation of a recurve array actuator205 driving a synthetic jet 400. A synthetic jet 400 generatesturbulence along a surface 420 by drawing air in and out through anopening 412 in the surface 420. FIG. 12A shows a synthetic jet 400driven by an exemplary recurve array actuator 205 of the presentinvention. In FIG. 12A, the recurve array actuator 205 is shown in therelaxed position, this is neither extended nor retracted. The recurvearray actuator 205 in FIGS. 12A, 12B, and 12C, by way of example and notlimitation, is suitably of the same configuration as the recurve arrayactuator described in FIGS. 9A and 9B above. The recurve array actuator205 has two recurve elements 207 and 209 that are driven throughelectrical connections 407 and 409 respectively. The electricalconnections cause the two recurve elements 207 and 209 to alternatelycurve toward each other in a retracted configuration as shown in FIG.12C, and curve away from each other in an extended form as shown in FIG.12B. The recurve array actuator 205 is connected to a diaphragm 410through a linkage 408 at the center 227 of recurve element 207. Asdescribed in connection with FIGS. 9A and 9B, the ends 231 of the firstrecurve element 207 are linked to the ends 231 of the second recurveelement 209. The center 217 of the second recurve element 209 is linkedto a base 210 which, in this embodiment, supports the array actuator 205and provides a fixed position from which the diaphragm 410 is driven bythe array actuator 205. The first recurve element 207 and the secondrecurve element 209 are driven through the electrical connections 407and 409 by a drive circuit (not shown) such as that described inconnection with FIGS. 1A and 1B. The first recurve element 207 and thesecond recurve element 20 may be driven at a periodic frequency whichmay be mechanically resonant for the first array element 207 and thesecond array element 209. This causes the diaphragm 410 to move back andforth with a greater amplitude that would occur if the periodicfrequency was not mechanically resonant. The first array element 207 andthe second array element 209 when resonate act as flat springs deflectedin alternate directions at their centers.

The diaphragm 410 is a flexible diaphragm of a suitable materialbridging the gap 412 in the surface 420. As the diaphragm 410 moves backand forth it draws air in and out of the synthetic jet 400, therebyinducing turbulence along the surface 420.

In FIG. 12B the recurve array actuator 205 is shown in the extendedposition with the first recurve element 207 curving away from the secondrecurve element 209. This forces the linkage 408 and the connecteddiaphragm 410 away from the base 210. This drives air out 444 of theopening or gap 412, thereby forming the synthetic jet 400.

In FIG. 12C, the recurve array actuator 205 is shown in the retractedposition where the first recurve element 207 and the second recurveelement 209 curve toward each other. This pulls the linkage 408 and theattached diaphragm 410 towards the base 210 and away from the surface420. This draws air in 442 to the opening 412 in the surface 420.Synthetic jets have a wide variety of aerodynamic applications includingplacement on air foils. For example, synthetic jets 400 can assistshaping air flows over such an air foil (not shown). It will beappreciated that multi-layer recurve actuators, as well as single layerrecurve actuators, suitably may be used to form the array driving thesynthetic jet 400.

It will be appreciated that embodiments of the recurve actuators of thepresent invention, such as those described in FIGS. 6, 7, and 8, themulti-layer recurve actuator as described in FIGS. 10 and 11, therecurve actuator array described in FIG. 9, and the synthetic jet systemdriven by a recurve actuator array in FIG. 12, may also be assembledusing multiple basic form electrostrictive actuators such as describedin FIGS. 1, 2, and 4, assembled or linked end-to-end. The recurve shapesof the recurve actuator, multi-layer recurve actuator, and recurveactuator array may be generated by four electrostrictive actuators ofequal size suitably assembled or attached end-to-end with the two endactuators curving one way, and the center two actuators curving theopposite direction when this compound actuator is activated. It will beappreciated that the lengths of the respective segments of such acompound actuator may be suitably varied if, for a desired application,the ends of the compound actuator need not remain parallel or co-planar.It will also be appreciated that the number of actuator segments in acompound actuator need not be four as in a recurve actuator, but may beany number depending upon the desired deflection and shape of deflectiondesired.

In general form, a compound actuator may have at least two actuatorsegments curving in opposite directions when the activating electricalfields V_(ab) and V_(ac) vary inversely to each other. A compoundactuator therefore has at least two oppositely driven actuator segmentsattached to each other so as to form an s-curve when activated. It willbe appreciated that two, two-segment, s-curve compound actuators placedend-to-end suitably form a recurve actuator as described above.Restated, a two-segment s-curve compound actuator is thus a half-recurveactuator. Such a two segment s-curve actuator can be understood byconsidering at either end half of the recurve actuator described inFIGS. 6, 7, and 8.

A compound actuator may also be described by its base unit including acombination of two adjoining, oppositely-driven electrostrictiveactuator segments that form an s-curve when activated. FIGS. 13A, 13B,and 13C show the operation of a compound actuator 505 with a firstsegment 570 and a second segment 572. In this exemplary embodiment, thecompound actuator 505 is a two segment s-curve actuator. The compoundactuator has, a first electrostrictive layer 512 and a secondelectrostrictive layer 516. It will be appreciated that compoundactuators may be assembled utilizing multiple layers of electrostrictivematerial in the manner described above in connection with a multi-layerrecurve actuator. In FIGS. 13A, 13B, and 13C, the compound actuator 505is shown in cross-section, showing deflections and dimensions in the xaxis 321-z axis 323 axes.

In this exemplary embodiment, the first segment 570 of the compoundactuator 505 is to the right and the second compound segment 572 of thecompound actuator 505 is to the left. The left end 560 of the compoundactuator 505 is held by a support 504 while the right end 562 of thecompound actuator 505 in this example is unrestrained and may move asthe compound actuator is activated. By way of example and notlimitation, the first segment 570 of the compound actuator has a length185 equalized to the length 185 of the second segment 572. Activation ofthe compound actuator 505 thus results in the deflection of the rightend 562 of the compound actuator 505 either up or down in the z-axisdirection 323, while the right end 562 of the compound actuator 505remains parallel to the left end 560 even as it deflects along thez-axis 323. Deflection of the compound actuator 505 in the up directionis shown in FIG. 13B, and deflection of the compound actuator 505 in thedown direction is shown in FIG. 13C. The electrode configuration of thecompound actuator 505 is similar to that of the electrostrictiveactuator described in FIGS. 1 and 2 and the recurve actuators describedin FIGS. 6, 7, and 8, and 10 and 11 above. Between the firstelectrostrictive layer 512 and the second electrostrictive layer 516 isan intermediate electrode sheet 540 driven at a voltage equal to V_(b).In this example, the first electrostrictive layer 512 is above theintermediate electrode sheet 540, and the second electrode sheet 516 isbelow the intermediate electrode sheet 540. It will be appreciated thatthe directions and axes utilized in connection with FIGS. 13A, 13B, and13C are for descriptive purposes only, and different referencedirections and axes and orientations of the actuators may be utilized todescribe or install the actuator in a device utilizing it.

The compound actuator 505 has two second electrode sheets 520, one abovethe first electrostrictive layer 512 and the other below the secondelectrostrictive layer 516. The compound actuator 505 has two secondelectrode sheets 520. This is because the upper electrode sheet 564,located above the first electrostrictive layer 512 is a second electrodesheet 520 with two sections 522 and 524. The bottom electrode sheet 568,below the second electrostrictive layer 516, is also a second electrodesheet 520, with the same configuration as the upper electrode sheet 564.However, the bottom electrode sheet 560 is rotated (not shown) asdescribed below in connection with FIGS. 14A and 14B. The exemplarycompound actuator 505 thus is a five-layer sandwich, which from the topor upper side to the lower or bottom includes a top electrode sheet 564including a second electrode sheet 520, the first electrostrictive layer512, the intermediate electrode sheet 540 which may also be labeled asthe middle electrode sheet 562, the second electrostrictive layer 516,and the bottom electrode sheet 568 including a second electrode sheet520. As noted, the bottom electrode sheet 568 is suitably in the sameoutline as the top electrode sheet 564, but is rotated and placed on thebottom of the compound actuator 505. As with the recurve actuatorsdescribed above, the electrostrictive layers and the electrode sheetsmay be attached to each other in any suitable manner such thatdifferential changes in the lengths of the electrostrictive layersresults in deflection of the compound actuator 505.

In this embodiment, the upper electrode sheet 564 has a first electrodesection 522 and a second electrode section 524 divided by a gap 529. Thelength 185 of the first electrode section 522 is equalized toward thelength 185 of the second electrode section 524. There is a gap 529between the two sections 522 and 524. This is because the two sections522 and 524 are driven at different voltages. In this example, the firstelectrode section 522 of the upper electrode sheet 564 to the right isdriven at a voltage equal to V_(c) in the first segment 570. The secondelectrode section 524 of the upper electrode sheet 564 to the left isdriven at a voltage equal to V_(a) in the second segment 572.

The entire middle electrode sheet 566 is driven at a voltage equal toV_(b). The lower electrode sheet 560, being a rotated second electrodesheet 520, is reversed right to left in the view in FIGS. 13A, 13B, and13C from the orientation of the upper electrode sheet 564. The lowerelectrode sheet 568 is driven opposite the upper electrode sheet 564.Thus the lower electrode sheet 568 has its second electrode section 524to the right 531 driven at a voltage equal to V_(a). The first electrodesection 522 of the lower electrode sheet 568 is to the left and isdriven at a voltage equal to V_(c).

In FIG. 13A, V_(ab) equals V_(bc), thus there is no deflection of thecompound actuator 505. The right end 562 of the compound actuator 505 isthus co-planar with the left end 560 of the compound actuator 505, andthere is no deflection.

FIG. 13B shows the compound actuator 505 of FIG. 13A when V_(ab) isgreater than V_(bc). As a result, the right end 562 of the compoundactuator 505 deflects upward along the z-axis 323 a deflection amount518. In this example, the deflection amount is denoted as a positive +Δ.

Deflection of the compound actuator 505 upward is caused by the firstsegment 570 forming a downward curve or a curve with a decreasing radiustowards the second electrostrictive layer 516. At the same time, thesecond segment 572 attached at its left end 560 to the support 504,curves upward. That is, the second segment 572 curves with a decreasingradius towards the first electrostrictive layer 512.

FIG. 13C is the converse of the FIG. 13B when V_(ab) is less thanV_(bc). In this configuration, the first segment 570 curves upward orwith a decreasing radius toward the first electrostrictive layer 112. Atthe same time, the second segment 572, curves downward or with adecreasing radius toward the second electrostrictive layer 516. Theresult is a deflection of the right end 562 downward in a deflectionamount 518 (in this instance denoted as a negative −Δ). In thedeflection of the compound actuator 505 shown in FIG. 13C, the right end562 remains substantially parallel to the left end 560 even as itdeflects. It will be appreciated that the right end 562 remainssubstantially parallel or co-planar to the left end 560 because the twooppositely curving segments 570 and 572 are of equalized length andcurve in an equalized amount, thereby forming a symmetrical s-curve.

FIGS. 13A, 13B, and 13C thus show the operation of a basic compoundactuator 505. It will be appreciated that the compound actuator may haveany suitable numbers of oppositely curving or driven actuator segments,depending upon the application and the desired shape of the deflectiondesired for the application.

A compound actuator may also be described symbolically, showing theelectrode sections and electrostrictive layer segments. FIG. 14A is asymbolic representation of the electrode sheets and the electrostrictivelayers of the compound actuator 505 of FIGS. 13A, 13B, and 13C. In FIG.14A, the compound actuator 505 is again shown in cross-section in thex-z plane with the x-axis 521 running right to left, and the z-axis 523running up to down. The compound actuator has, a first segment 570 tothe right and a second segment 572 to the left. The length 185 of thefirst segment 570 approximately equals the length 185 of the secondsegment 572. The right end 562 of the compound actuator 505 is to theright, and the left end 560 is to the left. The top electrode sheet 564is the upper most layer in the FIG. 14A, and the bottom electrode sheet568 is the lower-most layer. Both the upper electrode sheet 564 and thelower electrode sheet 568 include the same configuration of a secondelectrode sheet 520, but are rotated with respect to each other (notshown).

The second electrode sheet 520, utilized for both the upper electrodesheet 564 and the lower electrode sheet 568, has a first end 506 and asecond end 508. The second electrode sheet 520 includes a center gap 529separating the first electrode section 522 and the second electrodesection 524. The first electrode section 522 has a length 185 equalizedto the length of the second electrode section 524 equalized to thelengths of the two segments 570 and 572 of the compound actuator 505. Byway of example and not limitation, the second electrode sheet 520 is ina configuration of an intermediate electrode sheet 520 as shown in FIG.14B, described below. The electrode sections control the electricalfield experienced by the adjacent electrostrictive layers and thus formdifferent driven segments of the compound actuator 505. In thisexemplary embodiment, the first end 506 of the second electrode sheet520 forming the upper electrode sheet 564 is to the right, and thesecond end 508 of the second electrode sheet 520 forming the upperelectrode sheet 564 is to the left. The first electrode section 522 runsfrom the first end 506 to the gap 529 at the center 507. The secondelectrode section 524 runs from the gap 527 at the center 507 to thesecond end 508. In this configuration, the first electrode section 522of the upper electrode sheet 564 is to the right while the secondelectrode section 524 is to the left.

As in FIGS. 13A, 13B, and 13C, the compound actuator 505 in thisexemplary embodiment includes a five layer sandwich of the upperelectrode sheet 524, a first electrostrictive layer 512, a middleelectrode sheet 566, a second electrode sheet 516, and a lower electrodesheet 568, from the upper side to the lower side of the compoundactuator 505 along the z-axis 523. Thus, immediately below the upperelectrode sheet 564 is the first electrostrictive layer 512 andimmediately below the first electrostrictive layer 512 is theintermediate electrode sheet 566. By way of example but not limitation,the intermediate electrode sheet 566 is in a configuration 540 of anintermediate electrode sheet as shown in FIG. 14B, described below. Theentire intermediate electrode section 542 is driven at a voltage equalto V_(b).

The first electrode section 522 of the upper electrode sheet 564 isdriven at a voltage equal to V_(c), while the second electrode section524 of the upper electrode sheet 564 is driven at a voltage equal toV_(a). As a result, the first electrostrictive layer 512 experiences twodifferent electrical fields: an electrical field with the potentialvoltage equal to V_(bc) on the right; and an electrical field with avoltage potential equal to V_(ab) on the left. These fields correspondto the charges applied to the electrode sections of the upper electrodesheets 564 immediately above and the intermediate electrode sheet 566driven at a voltage V_(b) below. Thus the first electrostrictive layerhas a right segment 584 that experiences a voltage potential equal toV_(bc) and a left segment 586 experiencing a voltage potential equal toV_(ab).

Below the intermediate electrode layer 566 is the secondelectrostrictive layer 516. Below the second electrostrictive sheet isthe lower electrode sheet 568.

In this example, the ends 508 and 506 of second electrode sheet 520 arereversed right-to-left from the upper electrode sheet 564. Thus, thefirst end 506 of the second electrode sheet 520 that forms the lowerelectrode sheet 568 is on the left end 560, while the second end 508 ofthe second electrode sheet 520 forming the lower electrode sheet 568 ison the right end 562. The first section 522 to the left is driven with avoltage equal to V_(c). The second end section 524 to the right isdriven with a voltage equal to V_(a). As a result, the secondelectrostrictive layer 516 immediately above the lower electrode sheet568 and immediately below the middle electrode sheet 566 is driven withan electrical field of two different electrical potentials. A right handsegment 586 is driven at a voltage potential equal to V_(ab), and a lefthand segment 588 is driven at a voltage potential equal to V_(bc). Inthis configuration, as shown in FIGS. 13A, 13B, and 13C, as voltageV_(ab) and V_(bc) vary inversely to each other, the first segment 570and the second segment 572 of the compound actuator 505 curve inopposite directions.

It will be appreciated that a compound actuator may be driven with awide range of electrical configurations and layouts of connections.However, it will be appreciated that certain configurations and layoutsmay be more easily manufactured and assembled than other configurationsand layouts. FIG. 14B shows an exemplary configuration for the compoundactuator 505 of FIGS. 13A, 13B, 13C and 14A. FIG. 14B presents a topview of two electrode sheets that can be utilized to construct acompound actuator. In FIG. 14B the x-axis 521 runs from right to left.The x-axis 521 forms the centerline between the first end 506 and thesecond end 508 of the two electrode sheets, the intermediate electrodesheet 540, and the second electrode sheet 520. The x-y plane is shownwith the y-axis 525 running up and down. These axes correspond to theisometric views of the electrodes in FIG. 11. It will be appreciatedthat the intermediate electrode sheet 540 and the second electrode sheet520 are similar to end halves of the intermediate electrode sheet 140and the second electrode sheet 120 of FIG. 8B.

In FIG. 14B, the intermediate electrode sheet 540 has a first end 506, asecond end 508, and an electrode area 542 between the ends 506 and 508.Each end 506 and 508 has a connection tab 551 and 553, respectively,each with a connection point 545. The connection tabs 551 and 553 andthe connection points 545 are situated on the centerline or x-axis 521of the intermediate electrode sheet 540. The connection points 545 tothe intermediate electrode sheet 540 are driven at a voltage equal toV_(b) and are located at the centerline or x-axis 521 of theintermediate electrode sheet 540. Connections to V_(a) and V_(b) can bemade to electrode sheets above and below the intermediate electrodesheet 540 on alternate sides of the centerline and thus not overlap orshort out with each other, or with the connection points 545.

The second electrode sheet 520 has a first end 506 and a second end 508,with a first electrode section 522, a second electrode section 524, anda center gap 529 intermediate sections 522 and 524. The center gap 529at the center 507 between the two ends 506 and 508 permits the firstelectrode section 522 to be driven at a voltage different from thesecond electrode section 524. In this embodiment, the first electrodesection 522 at end 506 has a connection tab 541 and a connection point547. In this orientation, the electrode sheet 520 has its first end 506and its first electrode section 522 to the right forming a right end 562with a connection tab 541 and a connection point 547. The connection tab541 and the connection point 547 are located at the first end 506 downin the y-axis direction 525 in this top view from the x-axis 521 orcenterline of the second electrode sheet 520, and form the right end560. The connection tab 541 and the connection tab 547 are a suitabledistance from the centerline or x-axis 521 so as to not overlap with theconnection tab 551 and connection point 545 of the first end 506 of theintermediate electrode layer when a compound actuator (not shown) isassembled.

The second electrode sheet 520 in this orientation has a connection tab543 and a connection point 549 on its second end 508 that forms the leftend 560. The connection tab 543 and the connection point 549 are up inthe y-axis direction 525 in this top view away from the centerline orx-axis 521 of the second electrode sheet 520. A suitable distance ischosen so that the connection tab 543 and the connection point 549 donot overlap with the connection tab 553 and connection point 545 on thesecond end 508 of the intermediate electrode sheet 540 (which has itsconnection tab 553 and connection point 545 on the centerline or x-axis521).

FIG. 14B thus shows exemplary electrode sheet configurations that aresuitably utilized to assemble the compound actuator 505 of FIGS. 13A,13B, 13C, and 14A. In FIGS. 13A, 13B, 13C and 14A, the upper electrodesheet 564 is a second electrode sheet 520 in the orientation shown inFIG. 14B. The middle electrode sheet 566 of FIGS. 13A, 13B, 13C, and 14Ais the same shape as the intermediate electrode sheet 540 of FIG. 14B.The lower electrode sheet 568 in FIGS. 13A, 13B, 13C, and 14A is thesame shape as the second electrode sheet 520 of FIG. 14B, but isreoriented by rotating the electrode sheet 180 degrees around its x-axisor centerline 521. In this lower electrode sheet 568 configuration (notshown), the rotation places connection tab 541 and connection 547 up inthe y-axis 525 direction in top view from the centerline and x-axis 521on the right end 562, and places the left end connection tab 543 andconnection 549 down in the y-axis direction in top view from thecenterline or x-axis of the second electrode sheet 520. This permits theright end electrode section of the lower electrode sheet 568 to bedriven at a voltage of V_(a), while the left electrode section of thelower electrode sheet 568 in FIGS. 13 and 14 is driven at a voltageequal to V_(c). Thus, the compound actuator 505 of FIGS. 13 and 14 canbe assembled by manufacturing two second electrode sheets 520 and oneintermediate electrode sheet 540 and assembling them in theseorientations with respect to each other.

It will be appreciated that compound actuators 505 such as that in FIGS.13 and 14 with electrical configurations as described in FIG. 14B may beplaced end-to-end, thereby forming a compound actuator of any desiredlength. Further, the compound actuator can be constructed as amulti-layer actuator in the fashion described in connection with FIGS.10 and 11. Compound actuators, whether with two segments such as ans-curve actuator or with more segments, may also be combined into arraysutilizing multiple compound actuators to drive mechanical equipment orother devices.

While the preferred embodiment of the invention has been illustrated anddescribed, as noted above, many changes can be made without departingfrom the spirit and scope of the invention. Accordingly, the scope ofthe invention is not limited by the disclosure of the preferredembodiment. Instead, the invention should be determined entirely byreference to the claims that follow.

1. A system for a compound actuator, the system comprising: a firstelectrode layer including a first electrode section and a secondelectrode section; a second electrode layer including a third electrodesection, the third electrode section being arranged to overlap the firstand second sections; a first electrostrictive material configured tochange length in response to an applied electrical field, the firstelectrostrictive material being positioned between the first electrodelayer and the second electrode layer, the first electrostrictivematerial having a first length adjoining the first electrode section anda second length adjoining the second electrode section; a thirdelectrode layer including a fourth electrode section and a fifthelectrode section, the fourth and fifth electrode sections beingarranged to overlap the first and second electrode sections,respectively; a second electrostrictive material configured to changelength in response to an applied electrical field, the secondelectrostrictive material being positioned between the second electrodelayer and the third electrode layer, the second electrostrictivematerial having a third length adjoining the fourth electrode sectionand a fourth length adjoining the fifth electrode section; and a firstvoltage source arranged to provide a voltage differential between thefirst electrode section and the fourth electrode section, and betweenthe second electrode section and the fifth electrode section, thevoltage differential causing the first electrostrictive material and thesecond electrostrictive material to change from the first length, thesecond length, the third length and the fourth length to a fifth length,a sixth length, a seventh length, and an eighth length, respectively,that are shorter than the first length, the second length, the thirdlength, and the fourth length, respectively.
 2. The system of claim 1,wherein the first electrostrictive material and the secondelectrostrictive material each include at least one sheet ofelectrostrictive material.
 3. The system of claim 1, wherein the firstelectrode layer, the second electrode layer, and the third electrodelayer each include at least one sheet of conductive material. 4.(canceled)
 5. The system of claim 1, further comprising: a secondvoltage source arranged to provide a variable voltage to the secondelectrode layer, the variable voltage causing the first electrostrictivematerial to change from the fifth length towards a ninth length that isshorter than the fifth length and the sixth length towards a tenthlength that is longer than the sixth length when the secondelectrostrictive material changes from the seventh length towards aneleventh length that is longer than the seventh length and the eighthlength towards a twelfth length that is shorter than the eighth length,the variable voltage further causing the first electrostrictive materialto change from the fifth length towards a thirteenth length that islonger than the fifth length and the sixth length towards a fourteenthlength that is longer than the sixth length when the secondelectrostrictive material changes from the seventh length towards afifteenth length that is shorter than the seventh length and the eighthlength towards a sixteenth length that is longer than the eighth length.6. The system of claim 5, wherein the second voltage source includes abiased AC voltage source, such that the lateral motion is periodic. 7.The system of claim 6, wherein the lateral motion is resonant.
 8. Thesystem of claim 1, wherein the first electrode section includes a firstconnection tab, the second electrode section includes a secondconnection tab, the third electrode section includes a third connectiontab, the fourth electrode section includes a fourth connection tab, andthe fifth electrode section includes a fifth connection tab, the first,third, and fourth connection tabs being arranged to not overlap eachother and the second, third, and fifth connection tabs being arranged tonot overlap each other.
 9. The system of claim 1, wherein the firstelectrode section includes a first connection tab, the second electrodesection includes a second connection tab, the third electrode sectionincludes a third connection tab and a fourth connection tab, the fourthelectrode section includes a fifth connection tab, the fifth electrodesection includes a sixth connection tab, the first, third, and fifthconnection tabs being arranged to not overlap each other, and thesecond, fourth, and sixth connection tabs being arranged to not overlapeach other.
 10. The system of claim 9, wherein the third connection tabis located intermediate the first connection tab and the fourthconnection tab, and the sixth connection tab is located intermediate thesecond connection tab and the fifth connection tab.
 11. The system ofclaim 1, wherein the first electrostrictive material and the secondelectrostrictive material include one of grafted elastomers, ionicpolymers, ceramics, relaxor ferroelectric-ferroelectric solid statesolutions, lead zinc niobate-lead titanate, and electron irradiatedcopolymer polyvinylidene fluoride-trifluoroethyline.
 12. The system ofclaim 11, wherein the relaxor ferroelectric-ferroelectric solid-statesolutions include one of lead magnesium, PZN-PT electrostrictivecrystals, PMN-PT electrostrictive crystals, and complex perovskitecrystal analogs.
 13. The system of claim 1, wherein the firstelectrostrictive material and the second electrostrictive material areattached to each other with an attachment including adhesive.
 14. Thesystem of claim 13, wherein the adhesive includes at least one sheet ofadhesive film.
 15. The system of claim 1, wherein the first electrodesection has a first electrode length, the second electrode section has asecond electrode length, the third electrode section has a thirdelectrode length, the fourth electrode section has a fourth electrodelength, and the fifth electrode section has a fifth electrode length,the second, fourth and fifth electrode lengths being equalized towardthe first electrode length, and third electrode length being around twotimes the first electrode length.
 16. The system of claim 15, whereinthe lateral motion includes an s-curve. 17.-112. (canceled)
 113. Asystem for a compound actuator, the system comprising: a first electrodelayer including a first electrode section and a second electrodesection; a second electrode layer including a third electrode section,the third electrode section being arranged to overlap the first andsecond sections; a first electrostrictive material configured to changelength in response to an applied electrical field, the firstelectrostrictive material being positioned between the first electrodelayer and the second electrode layer, the first electrostrictivematerial having a first length adjoining the first electrode section anda second length adjoining the second electrode section; a thirdelectrode layer including a fourth electrode section and a fifthelectrode section, the fourth and fifth electrode sections beingarranged to overlap the first and second electrode sections,respectively; a second electrostrictive material configured to changelength in response to an applied electrical field, the secondelectrostrictive material being positioned between the second electrodelayer and the third electrode layer, the second electrostrictivematerial having a third length adjoining the fourth electrode sectionand a fourth length adjoining the fifth electrode section, the secondelectrostrictive material and the first electrostrictive material beingattached to each other such that a first differential change in thefirst length and the third length and a second differential change inthe second length and the fourth length results in an s-curving of thefirst electrostrictive material and the second electrostrictivematerial; and a first voltage source arranged to provide a voltagedifferential between the first electrode section and the fourthelectrode section, and between the second electrode section and thefifth electrode section, the voltage differential causing the firstelectrostrictive material and the second electrostrictive material tochange from the first length, the second length, the third length andthe fourth length to a fifth length, a sixth length, a seventh length,and an eighth length, respectively, that are shorter than the firstlength, the second length, the third length, and the fourth length,respectively.
 114. (canceled)
 115. The system of claim 113, furthercomprising: a second voltage source arranged to provide a variablevoltage to the second electrode layer, the variable voltage causing thefirst electrostrictive material to change from the fifth length towardsa ninth length that is shorter than the fifth length and the sixthlength towards a tenth length that is longer than the sixth length whenthe second electrostrictive material changes from the seventh lengthtowards an eleventh length that is longer than the seventh length andthe eighth length towards a twelfth length that is shorter than theeighth length, the variable voltage further causing the firstelectrostrictive material to change from the fifth length towards athirteenth length that is longer than the fifth length and the sixthlength towards a fourteenth length that is longer than the sixth lengthwhen the second electrostrictive material changes from the seventhlength towards a fifteenth length that is shorter than the seventhlength and the eighth length towards a sixteenth length that is longerthan the eighth length.
 116. The system of claim 115, wherein the secondvoltage source includes a biased AC voltage source, such that thes-curving is periodic.
 117. The system of claim 116, wherein thes-curving motion is resonant.
 118. The system of claim 113, wherein thefirst electrostrictive material and the second electrostrictive materialinclude one of grafted elastomers, ionic polymers, ceramics, relaxorferroelectric-ferroelectric solid state solutions, lead zincniobate-lead titanate, and electron irradiated copolymer polyvinylidenefluoride-trifluoroethyline.
 119. The system of claim 118, wherein therelaxor ferroelectric-ferroelectric solid-state solutions include one oflead magnesium, PZN-PT electrostrictive crystals, PMN-PTelectrostrictive crystals, and complex perovskite crystal analogs. 120.The system of claim 113, wherein the first electrostrictive material andthe second electrostrictive material each include at least one sheet ofelectrostrictive material.
 121. The system of claim 1, wherein thesecond electrostrictive material and the first electrostrictive materialare attached to each other such that at least one differential change inthe first length and the third length, and the second length and thefourth length, respectively, results in a lateral motion of the firstelectrostrictive material and the second electrostrictive material.